UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM N-Q

       QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT
                               INVESTMENT COMPANY

                  Investment Company Act file number 811-22528
                                                    -----------

                     First Trust Energy Infrastructure Fund
           ---------------------------------------------------------
               (Exact name of registrant as specified in charter)

                       120 East Liberty Drive, Suite 400
                               Wheaton, IL 60187
           ---------------------------------------------------------
              (Address of principal executive offices) (Zip code)

                             W. Scott Jardine, Esq.
                          First Trust Portfolios L.P.
                       120 East Liberty Drive, Suite 400
                               Wheaton, IL 60187
           ---------------------------------------------------------
                    (Name and address of agent for service)

        Registrant's telephone number, including area code: 630-765-8000
                                                           --------------

                      Date of fiscal year end: November 30
                                              -------------

                  Date of reporting period: August 31, 2016
                                           -------------------

Form N-Q is to be used by management investment companies, other than small
business investment companies registered on Form N-5 (ss.ss. 239.24 and 274.5 of
this chapter), to file reports with the Commission, not later than 60 days after
the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under
the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use
the information provided on Form N-Q in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and
the Commission will make this information public. A registrant is not required
to respond to the collection of information contained in Form N-Q unless the
Form displays a currently valid Office of Management and Budget ("OMB") control
number. Please direct comments concerning the accuracy of the information
collection burden estimate and any suggestions for reducing the burden to the
Secretary, Securities and Exchange Commission, 100 F Street, NE, Washington, DC
20549. The OMB has reviewed this collection of information under the clearance
requirements of 44 U.S.C. ss. 3507.





ITEM 1. SCHEDULE OF INVESTMENTS. The Schedule(s) of Investments is attached
herewith.

FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS
AUGUST 31, 2016 (UNAUDITED)



    SHARES                                   DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
COMMON STOCKS - 89.1%

                                                                                 
                 ELECTRIC UTILITIES - 22.8%
        210,000  American Electric Power Co., Inc. (a)...............................  $   13,559,700
         78,600  Duke Energy Corp. (a)...............................................       6,261,276
        178,600  Emera, Inc. (CAD) (a)...............................................       6,503,088
        203,400  Eversource Energy (a)...............................................      10,977,498
        241,100  Exelon Corp. (a)....................................................       8,197,400
        149,900  Fortis, Inc. (CAD) (a)..............................................       4,715,095
         54,200  Hydro One Ltd. (CAD) (a) (b)........................................       1,083,669
         58,200  IDACORP, Inc. (a)...................................................       4,427,274
        111,000  NextEra Energy, Inc. (a)............................................      13,424,340
        124,700  Southern (The) Co. (a)..............................................       6,400,851
         55,900  Xcel Energy, Inc. (a)...............................................       2,312,024
                                                                                       --------------
                                                                                           77,862,215
                                                                                       --------------

                 GAS UTILITIES - 2.7%
          5,800  Atmos Energy Corp. (a)..............................................         427,460
         86,610  Chesapeake Utilities Corp. (a)......................................       5,512,726
         54,000  New Jersey Resources Corp. (a)......................................       1,816,560
         18,100  ONE Gas, Inc. (a)...................................................       1,108,263
          8,718  UGI Corp. ..........................................................         396,495
                                                                                       --------------
                                                                                            9,261,504
                                                                                       --------------

                 MULTI-UTILITIES - 18.0%
         61,300  Alliant Energy Corp. (a)............................................       2,326,335
        145,800  ATCO, Ltd., Class I (CAD) (a).......................................       5,348,817
        163,400  Canadian Utilities Ltd., Class A (CAD) (a)..........................       4,684,947
        113,300  CMS Energy Corp. ...................................................       4,755,201
        151,500  National Grid PLC, ADR (a)..........................................      10,527,735
        162,400  NiSource, Inc. (a)..................................................       3,887,856
        255,900  Public Service Enterprise Group, Inc. (a)...........................      10,942,284
         98,400  SCANA Corp. (a).....................................................       6,951,960
         55,300  Sempra Energy (a)...................................................       5,786,039
        104,700  WEC Energy Group, Inc. (a)..........................................       6,269,436
                                                                                       --------------
                                                                                           61,480,610
                                                                                       --------------

                 OIL, GAS & CONSUMABLE FUELS - 45.6%
      1,700,363  Enbridge Energy Management, LLC (a) (c).............................      38,700,262
        616,300  Enbridge Income Fund Holdings, Inc. (CAD) (a).......................      14,798,907
        230,269  Enbridge, Inc. (a)..................................................       9,093,323
        361,700  Inter Pipeline, Ltd. (CAD) (a)......................................       7,866,161
        155,600  Keyera Corp. (CAD) (a)..............................................       4,804,212
      1,112,675  Kinder Morgan, Inc. (a).............................................      24,311,949
        225,200  ONEOK, Inc. (a).....................................................      10,559,628
         35,900  Spectra Energy Corp. (a)............................................       1,278,758
         51,100  Targa Resources Corp (a)............................................       2,226,938
        600,570  TransCanada Corp. (a)...............................................      27,295,907
        528,500  Williams (The) Cos., Inc. (a).......................................      14,766,290
                                                                                       --------------
                                                                                          155,702,335
                                                                                       --------------
                 TOTAL COMMON STOCKS ................................................     304,306,664
                 (Cost $291,710,936)                                                   --------------



                        See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
AUGUST 31, 2016 (UNAUDITED)



    SHARES                                   DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
MASTER LIMITED PARTNERSHIPS - 34.7%

                                                                                 
                 CHEMICALS - 0.1%
         21,000  Westlake Chemical Partners, L.P. (a)................................  $      488,670
                                                                                       --------------

                 GAS UTILITIES - 2.7%
        114,152  AmeriGas Partners, L.P. (a).........................................       5,231,586
        118,900  Suburban Propane Partners, L.P. (a).................................       3,941,535
                                                                                       --------------
                                                                                            9,173,121
                                                                                       --------------

                 INDEPENDENT POWER AND RENEWABLE ELECTRICITY PRODUCERS - 3.6%
        417,455  NextEra Energy Partners, L.P. (a) (d)...............................      12,160,464
                                                                                       --------------

                 OIL, GAS & CONSUMABLE FUELS - 28.3%
        139,700  Alliance Holdings GP, L.P. (a)......................................       3,500,882
        333,130  Alliance Resource Partners, L.P. (a)................................       6,792,521
         61,700  Buckeye Partners, L.P. (a)..........................................       4,335,042
        245,800  Columbia Pipeline Partners, L.P. (a)................................       3,335,506
         36,600  Enbridge Energy Partners, L.P. (a)..................................         851,316
        637,700  Enterprise Products Partners, L.P. (a)..............................      16,835,280
        122,200  EQT Midstream Partners, L.P. (a)....................................       9,606,142
        200,676  Holly Energy Partners, L.P. (a).....................................       6,527,990
         59,300  Magellan Midstream Partners, L.P. (a)...............................       4,170,569
        115,972  NGL Energy Partners, L.P. (a).......................................       2,103,732
        144,800  ONEOK Partners, L.P. (a)............................................       5,611,000
        231,386  Plains All American Pipeline, L.P. (a)..............................       6,492,691
          5,000  Shell Midstream Partners, L.P. .....................................         152,350
        179,300  Spectra Energy Partners, L.P. (a)...................................       8,181,459
         44,328  Tallgrass Energy Partners, L.P. (a).................................       2,042,634
        167,195  TC PipeLines, L.P. (a)..............................................       8,779,410
         52,002  TransMontaigne Partners, L.P. (a)...................................       2,177,844
        133,138  Williams Partners, L.P. (a).........................................       5,072,558
                                                                                       --------------
                                                                                           96,568,926
                                                                                       --------------
                 TOTAL MASTER LIMITED PARTNERSHIPS ..................................     118,391,181
                 (Cost $100,770,719)                                                   --------------

REAL ESTATE INVESTMENT TRUSTS - 1.1%

                 REAL ESTATE INVESTMENT TRUSTS - 1.1%
        128,550  InfraREIT, Inc. (a).................................................       2,429,595
         46,101  CorEnergy Infrastructure Trust, Inc. ...............................       1,356,291
                                                                                       --------------
                 TOTAL REAL ESTATE INVESTMENT TRUSTS ................................       3,785,886
                 (Cost $4,332,396)                                                     --------------

                 TOTAL INVESTMENTS - 124.9% .........................................     426,483,731
                 (Cost $396,814,051) (e)                                               --------------

   NUMBER OF
   CONTRACTS                                 DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
CALL OPTIONS WRITTEN - (0.8%)
                 American Electric Power Co., Inc. Calls
            700  @ $70.00 due September 2016 (f).....................................          (1,400)



                        See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
AUGUST 31, 2016 (UNAUDITED)



   NUMBER OF
   CONTRACTS                                 DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
CALL OPTIONS WRITTEN (CONTINUED)
                                                                                 
                 American Electric Power Co., Inc. Calls (Continued)
            800  @ $72.50 due November 2016..........................................  $       (8,000)
                                                                                       --------------
                                                                                               (9,400)
                                                                                       --------------
                 CMS Energy Corp. Call
          1,060  @  45.00 due September 2016 (f).....................................          (1,060)
                                                                                       --------------
                 Duke Energy Corp. Calls
            200  @  87.50 due September 2016 (f).....................................          (1,000)
            300  @  87.50 due January 2017...........................................         (15,600)
                                                                                       --------------
                                                                                              (16,600)
                                                                                       --------------
                 Enbridge, Inc. Calls
            200  @  42.50 due September 2016.........................................            (200)
            100  @  42.50 due October 2016...........................................          (3,500)
            600  @  45.00 due October 2016 (f).......................................         (18,000)
            800  @  45.00 due January 2017 (f).......................................         (64,000)
                                                                                       --------------
                                                                                              (85,700)
                                                                                       --------------
                 Eversource Energy Calls
            200  @  60.00 due September 2016 (f).....................................          (1,000)
          1,200  @  65.00 due January 2017 (f).......................................         (54,000)
                                                                                       --------------
                                                                                              (55,000)
                                                                                       --------------
                 Exelon Corp. Calls
            200  @  39.00 due September 2016 (f).....................................          (1,000)
          1,100  @  37.00 due October 2016...........................................          (8,250)
            400  @  38.00 due October 2016 (f).......................................          (1,600)
            100  @  37.00 due January 2017...........................................          (4,500)
                                                                                       --------------
                                                                                              (15,350)
                                                                                       --------------
                 Kinder Morgan, Inc. Calls
          9,200  @  20.00 due September 2016.........................................      (1,674,400)
            200  @  21.00 due September 2016.........................................         (19,800)
                                                                                       --------------
                                                                                           (1,694,200)
                                                                                       --------------
                 ONEOK, Inc. Call
          1,900  @  52.50 due October 2016...........................................         (61,750)
                                                                                       --------------
                 Plains All American Pipeline L.P. Calls
            600  @  31.00 due October 2016...........................................         (21,000)
          1,300  @  32.00 due October 2016 (f).......................................         (39,000)
                                                                                       --------------
                                                                                              (60,000)
                                                                                       --------------
                 SCANA Corp. Call
            600  @  80.00 due November 2016 (f)......................................         (21,000)
                                                                                       --------------
                 Sempra Energy Call
            300  @  115.00 due September 2016 (f)....................................          (1,500)
                                                                                       --------------
                 Southern (The) Co. Calls
            300  @  57.50 due November 2016..........................................          (2,400)



                        See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
AUGUST 31, 2016 (UNAUDITED)



   NUMBER OF
   CONTRACTS                                 DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
CALL OPTIONS WRITTEN (CONTINUED)
                                                                                 
                 Southern (The) Co. Calls (Continued)
            500  @ $55.00 due January 2017...........................................  $      (27,500)
                                                                                       --------------
                                                                                              (29,900)
                                                                                       --------------
                 Spectra Energy Corp. Call
            200  @  38.00 due December 2016..........................................         (10,500)
                                                                                       --------------
                 TransCanada Corp. Calls
          2,600  @  50.00 due September 2016.........................................         (23,400)
          1,100  @  50.00 due November 2016..........................................         (16,500)
            800  @  50.00 due January 2017...........................................         (32,000)
                                                                                       --------------
                                                                                              (71,900)
                                                                                       --------------
                 Williams (The) Cos., Inc. Calls
          1,200  @  25.00 due September 2016.........................................        (360,000)
            700  @  26.00 due September 2016.........................................        (119,000)
          1,000  @  27.00 due September 2016.........................................        (124,000)
          1,400  @  28.00 due September 2016.........................................         (82,600)
            100  @  30.00 due October 2016...........................................          (7,300)
                                                                                       --------------
                                                                                             (692,900)
                                                                                       --------------
                 Xcel Energy Inc. Call
            300  @  45.00 due September 2016 (f).....................................          (3,000)
                                                                                       --------------
                 TOTAL CALL OPTIONS WRITTEN .........................................      (2,829,760)
                 (Premiums received $1,745,080)                                        --------------

                 OUTSTANDING LOAN - (35.6%) .........................................    (121,500,000)

                 NET OTHER ASSETS AND LIABILITIES - 11.5% ...........................      39,366,460
                                                                                       --------------
                 NET ASSETS - 100.0% ................................................  $  341,520,431
                                                                                       ==============


-----------------------------

(a)   All or a portion of this security serves as collateral on the outstanding
      loan.

(b)   This security is restricted in the U.S. and cannot be offered for public
      sale without first being registered under the Securities Act of 1933, as
      amended. This security is not restricted on the foreign exchange where it
      trades freely without any additional registration. As such, it does not
      require the additional disclosure required of restricted securities.

(c)   Non-income producing security that makes payment-in-kind ("PIK")
      distributions. For the fiscal year-to-date period (December 1, 2015
      through August 31, 2016), the fund received 131,527 PIK shares of Enbidge
      Energy Management, LLC.

(d)   NextEra Energy Partners, L.P. is taxed as a "C" corporation for federal
      income tax purposes.

(e)   Aggregate cost for financial reporting purposes, which approximates the
      aggregate cost for federal income tax purposes. As of August 31, 2016, the
      aggregate gross unrealized appreciation for all securities in which there
      was an excess of value over tax cost was $39,938,903 and the aggregate
      gross unrealized depreciation for all securities in which there was an
      excess of tax cost over value was $10,269,223.

(f)   This security is fair valued by the First Trust Advisors L.P.'s Pricing
      Committee in accordance with procedures adopted by the Fund's Board of
      Trustees and in accordance with provisions of the Investment Company Act
      of 1940, as amended. At August 31, 2016, securities noted as such are
      valued at $(207,560) or (0.06)% of net assets.


                        See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
AUGUST 31, 2016 (UNAUDITED)

ADR   American Depositary Receipt

CAD   Canadian Dollar - Security is denominated in Canadian Dollars and is
      translated into U.S. Dollars based upon the current exchange rate.

-----------------------------

INTEREST RATE SWAP AGREEMENTS:


                                                                  NOTIONAL
   COUNTERPARTY        FLOATING RATE (1)    EXPIRATION DATE        AMOUNT        FIXED RATE (1)       VALUE
---------------------------------------------------------------------------------------------------------------
                                                                                     
Bank of Nova Scotia      1 month LIBOR         10/08/20        $   36,475,000        2.121%        $ (1,759,089)
Bank of Nova Scotia      1 month LIBOR         09/03/24            36,475,000        2.367%          (3,370,155)
                                                               --------------                      ------------
                                                               $   72,950,000                      $ (5,129,244)
                                                               ==============                      ============



(1)   The Fund pays the fixed rate and receives the floating rate. The floating
      rate on August 31, 2016 was 0.498% and 0.494%, respectively.

VALUATION INPUTS

A summary of the inputs used to value the Fund's investments as of August 31,
2016 is as follows (see Note 2A - Portfolio Valuation in the Notes to Portfolio
of Investments):



                                                    ASSETS TABLE
                                                                                        LEVEL 2           LEVEL 3
                                                     TOTAL            LEVEL 1         SIGNIFICANT       SIGNIFICANT
                                                   VALUE AT           QUOTED          OBSERVABLE       UNOBSERVABLE
                                                   8/31/2016          PRICES            INPUTS            INPUTS
                                                ---------------   ---------------   ---------------   ---------------
                                                                                          
Common Stocks*................................  $   304,306,664   $   304,306,664   $            --   $            --
Master Limited Partnerships*..................      118,391,181       118,391,181                --                --
Real Estate Investment Trusts*................        3,785,886         3,785,886                --                --
                                                ---------------   ---------------   ---------------   ---------------
Total Investments.............................  $   426,483,731   $   426,483,731   $            --   $            --
                                                ===============   ===============   ===============   ===============

                                                  LIABILITIES TABLE
                                                                                        LEVEL 2           LEVEL 3
                                                     TOTAL            LEVEL 1         SIGNIFICANT       SIGNIFICANT
                                                   VALUE AT           QUOTED          OBSERVABLE       UNOBSERVABLE
                                                   8/31/2016          PRICES            INPUTS            INPUTS
                                                ---------------   ---------------   ---------------   ---------------
Call Options Written..........................  $    (2,829,760)  $    (2,622,200)  $      (207,560)  $            --
Interest Rate Swaps**.........................       (5,129,244)               --        (5,129,244)               --
                                                ---------------   ---------------   ---------------   ---------------
                                                $    (7,959,004)  $    (2,622,200)  $    (5,336,804)  $            --
                                                ===============   ===============   ===============   ===============


*  See Portfolio of Investments for industry breakout.
** See Interest Rate Swap Agreements for contract detail.

All transfers in and out of the Levels during the period are assumed to be
transferred on the last day of the period at their current value. There were no
transfers between Levels at August 31, 2016.


                        See Notes to Portfolio of Investments





NOTES TO PORTFOLIO OF INVESTMENTS

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2016 (UNAUDITED)


                                1. ORGANIZATION

First Trust Energy Infrastructure Fund (the "Fund") is a non-diversified,
closed-end management investment company organized as a Massachusetts business
trust on February 22, 2011 and is registered with the Securities and Exchange
Commission under the Investment Company Act of 1940, as amended (the "1940
Act"). The Fund trades under the ticker symbol FIF on the New York Stock
Exchange ("NYSE").

The Fund, which is an investment company within the scope of Financial
Accounting Standards Board ("FASB") Accounting Standards Update 2013-08, follows
accounting and reporting guidance under FASB Accounting Standards Codification
Topic 946, "Financial Services-Investment Companies."

                     2. VALUATION AND INVESTMENT PRACTICES

A. PORTFOLIO VALUATION

The net asset value ("NAV") of the Common Shares of the Fund is determined daily
as of the close of regular trading on the NYSE, normally 4:00 p.m. Eastern time,
on each day the NYSE is open for trading. If the NYSE closes early on a
valuation day, the NAV is determined as of that time. Foreign securities are
priced using data reflecting the earlier closing of the principal markets for
those securities. The Fund's NAV per Common Share is calculated by dividing the
value of all assets of the Fund (including accrued interest and dividends), less
all liabilities (including accrued expenses, dividends declared but unpaid and
any borrowings of the Fund) by the total number of Common Shares outstanding.

The Fund's investments are valued daily at market value or, in the absence of
market value with respect to any portfolio securities, at fair value. Market
value prices represent last sale or official closing prices from a national or
foreign exchange (i.e., a regulated market) and are primarily obtained from
third-party pricing services. Fair value prices represent any prices not
considered market value prices and are either obtained from a third-party
pricing service or are determined by the Pricing Committee of the Fund's
investment advisor, First Trust Advisors L.P. ("First Trust" or the "Advisor"),
in accordance with valuation procedures adopted by the Fund's Board of Trustees,
and in accordance with provisions of the 1940 Act. Investments valued by the
Advisor's Pricing Committee, if any, are footnoted as such in the footnotes to
the Portfolio of Investments. The Fund's investments are valued as follows:

      Common stocks, master limited partnerships ("MLPs"), real estate
      investment trusts ("REITs"), and other equity securities listed on any
      national or foreign exchange (excluding The Nasdaq Stock Market LLC
      ("Nasdaq") and the London Stock Exchange Alternative Investment Market
      ("AIM")) are valued at the last sale price on the exchange on which they
      are principally traded, or for Nasdaq and AIM securities, the official
      closing price. Securities traded on more than one securities exchange are
      valued at the last sale price or official closing price, as applicable, at
      the close of the securities exchange representing the principal market for
      such securities.

      Exchange-traded options contracts are valued at the closing price in the
      market where such contracts are principally traded. If no closing price is
      available, exchange-traded options contracts are fair valued at the mean
      of their most recent bid and asked price, if available, and otherwise at
      their closing bid price. Over-the-counter options contracts are fair
      valued at the mean of their most recent bid and asked price, if available,
      and otherwise their closing bid price.

      Securities traded in an over-the-counter market are fair valued at the
      mean of their most recent bid and asked price, if available, and otherwise
      at their closing bid price.

      Swaps are fair valued utilizing quotations provided by a third-party
      pricing service or, if the pricing service does not provide a value, by
      quotes provided by the selling dealer or financial institution.

Certain securities may not be able to be priced by pre-established pricing
methods. Such securities may be valued by the Fund's Board of Trustees or its
delegate, the Advisor's Pricing Committee, at fair value. These securities
generally include, but are not limited to, restricted securities (securities
which may not be publicly sold without registration under the Securities Act of
1933, as amended (the "1933 Act")) for which a pricing service is unable to
provide a market price; securities whose trading has been formally suspended; a
security whose market or fair value price is not available from a
pre-established pricing source; a security with respect to which an event has
occurred that is likely to materially affect the value of the security after the
market has closed but before the calculation of the Fund's NAV or make it
difficult or impossible to obtain a reliable market quotation; and a security
whose price, as provided by the pricing service, does not reflect the security's
fair value. As a general principle, the current fair value of a security would
appear to be the amount which the owner might reasonably expect to receive for
the security upon its current sale. When fair value prices are used, generally
they will differ from market quotations or official closing prices on the
applicable exchanges. A variety of factors may be considered in determining the
fair value of such securities, including, but not limited to, the following:

      1)    the type of security;

      2)    the size of the holding;

      3)    the initial cost of the security;





NOTES TO PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2016 (UNAUDITED)


      4)    transactions in comparable securities;

      5)    price quotes from dealers and/or pricing services;

      6)    relationships among various securities;

      7)    information obtained by contacting the issuer, analysts, or the
            appropriate stock exchange;

      8)    an analysis of the issuer's financial statements; and

      9)    the existence of merger proposals or tender offers that might affect
            the value of the security.

If the securities in question are foreign securities, the following additional
information may be considered:

      1)    the value of similar foreign securities traded on other foreign
            markets;

      2)    ADR trading of similar securities;

      3)    closed-end fund trading of similar securities;

      4)    foreign currency exchange activity;

      5)    the trading prices of financial products that are tied to baskets of
            foreign securities;

      6)    factors relating to the event that precipitated the pricing problem;

      7)    whether the event is likely to recur; and

      8)    whether the effects of the event are isolated or whether they affect
            entire markets, countries or regions.

The Fund is subject to fair value accounting standards that define fair value,
establish the framework for measuring fair value and provide a three-level
hierarchy for fair valuation based upon the inputs to the valuation as of the
measurement date. The three levels of the fair value hierarchy are as follows:

      o     Level 1 - Level 1 inputs are quoted prices in active markets for
            identical investments. An active market is a market in which
            transactions for the investment occur with sufficient frequency and
            volume to provide pricing information on an ongoing basis.

      o     Level 2 - Level 2 inputs are observable inputs, either directly or
            indirectly, and include the following:

            o     Quoted prices for similar investments in active markets.

            o     Quoted prices for identical or similar investments in markets
                  that are non-active. A non-active market is a market where
                  there are few transactions for the investment, the prices are
                  not current, or price quotations vary substantially either
                  over time or among market makers, or in which little
                  information is released publicly.

            o     Inputs other than quoted prices that are observable for the
                  investment (for example, interest rates and yield curves
                  observable at commonly quoted intervals, volatilities,
                  prepayment speeds, loss severities, credit risks, and default
                  rates).

            o     Inputs that are derived principally from or corroborated by
                  observable market data by correlation or other means.

      o     Level 3 - Level 3 inputs are unobservable inputs. Unobservable
            inputs may reflect the reporting entity's own assumptions about the
            assumptions that market participants would use in pricing the
            investment.

The inputs or methodologies used for valuing investments are not necessarily an
indication of the risk associated with investing in those investments. A summary
of the inputs used to value the Fund's investments as of August 31, 2016, is
included with the Fund's Portfolio of Investments.

B. OPTION CONTRACTS

The Fund is subject to equity price risk in the normal course of pursuing its
investment objective and may write (sell) options to hedge against changes in
the value of equities. Also, the Fund seeks to generate additional income, in
the form of premiums received, from writing (selling) the options. The Fund may
write (sell) covered call or put options ("options") on all or a portion of the
common stock and MLPs held in the Fund's portfolio as determined to be
appropriate by Energy Income Partners, LLC ("EIP" or the "Sub-Advisor"). The
number of options the Fund can write (sell) is limited by the amount of common
stock and MLPs the Fund holds in its portfolio. The Fund will not write (sell)
"naked" or uncovered options. Options are marked-to-market daily and their value
will be affected by changes in the value and dividend rates of the underlying
equity securities, changes in interest rates, changes in the actual or perceived
volatility of the securities markets and the underlying equity securities and
the remaining time to the options' expiration. The value of options may also be
adversely affected if the market for the options becomes less liquid or trading
volume diminishes.

Options the Fund writes (sells) will either be exercised, expire or be cancelled
pursuant to a closing transaction. If the price of the underlying equity
security exceeds the option's exercise price, it is likely that the option
holder will exercise the option. If an option written (sold) by the Fund is
exercised, the Fund would be obligated to deliver the underlying equity security
to the option holder upon payment of the strike price. In this case, the option
premium received by the Fund will be added to the amount realized on the sale of
the underlying security for purposes of determining gain or loss. If the price
of the underlying equity security is less than the option's strike price, the
option will likely expire without being exercised. The option premium received
by the Fund will, in this case, be treated as short-term capital gain on the
expiration date of the option. The Fund may also elect to close out its position
in an option prior to its expiration by purchasing an option of the same series
as the option written (sold) by the Fund.





NOTES TO PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2016 (UNAUDITED)


The options that the Fund writes (sells) give the option holder the right, but
not the obligation, to purchase a security from the Fund at the strike price on
or prior to the option's expiration date. The ability to successfully implement
the writing (selling) of covered call options depends on the ability of the
Sub-Advisor to predict pertinent market movements, which cannot be assured.
Thus, the use of options may require the Fund to sell portfolio securities at
inopportune times or for prices other than current market value, which may limit
the amount of appreciation the Fund can realize on an investment, or may cause
the Fund to hold a security that it might otherwise sell. As the writer (seller)
of a covered option, the Fund foregoes, during the option's life, the
opportunity to profit from increases in the market value of the security
covering the option above the sum of the premium and the strike price of the
option, but has retained the risk of loss should the price of the underlying
security decline. The writer (seller) of an option has no control over the time
when it may be required to fulfill its obligation as a writer (seller) of the
option. Once an option writer (seller) has received an exercise notice, it
cannot effect a closing purchase transaction in order to terminate its
obligation under the option and must deliver the underlying security to the
option holder at the exercise price.

Over-the-counter options have the risk of the potential inability of
counterparties to meet the terms of their contracts. The Fund's maximum equity
price risk for purchased options is limited to the premium initially paid. In
addition, certain risks may arise upon entering into option contracts including
the risk that an illiquid secondary market will limit the Fund's ability to
close out an option contract prior to the expiration date and that a change in
the value of the option contract may not correlate exactly with changes in the
value of the securities hedged.

C. SWAP AGREEMENTS

The Fund may enter into total return equity swap and interest rate swap
agreements. A swap is a financial instrument that typically involves the
exchange of cash flows between two parties ("Counterparties") on specified dates
(settlement dates) where the cash flows are based on agreed upon prices, rates,
etc. Swap agreements are individually negotiated and involve the risk of the
potential inability of the Counterparties to meet the terms of the agreement. In
connection with these agreements, cash and securities may be identified as
collateral in accordance with the terms of the respective swap agreements to
provide assets of value and recourse in the event of default under the swap
agreement or bankruptcy/insolvency of a party to the swap agreement. In the
event of a default by a Counterparty, the Fund will seek withdrawal of the
collateral and may incur certain costs exercising its rights with respect to the
collateral. If a Counterparty becomes bankrupt or otherwise fails to perform its
obligations due to financial difficulties, the Fund may experience significant
delays in obtaining any recovery in a bankruptcy or other reorganization
proceeding. The Fund may obtain only limited recovery or may obtain no recovery
in such circumstances.

Swap agreements may increase or decrease the overall volatility of the
investments of the Fund. The performance of swap agreements may be affected by
changes in the specific interest rate, security, currency, or other factors that
determine the amounts of payments due to and from the Fund. The Fund's maximum
equity price risk to meet its future payments under swap agreements outstanding
at August 31, 2016 is equal to the total notional amount as shown on the
Portfolio of Investments. The notional amount represents the U.S. dollar value
of the contract as of the day of the opening transaction or contract reset.

The Fund held interest rate swap agreements at August 31, 2016 to hedge against
changes in borrowing rates under the Fund's committed facility agreement. An
interest rate swap agreement involves the Fund's agreement to exchange a stream
of interest payments for another party's stream of cash flows. Interest rate
swaps do not involve the delivery of securities or other underlying assets or
principal. Accordingly, the risk of loss with respect to interest rate swaps is
limited to the net amount of interest payments that the Fund is contractually
obligated to make.

D. SECURITIES TRANSACTIONS

Securities transactions are recorded as of the trade date. Realized gains and
losses from securities transactions are recorded on the identified cost basis.

E. FOREIGN CURRENCY

The books and records of the Fund are maintained in U.S. dollars. Foreign
currencies, investments and other assets and liabilities are translated into
U.S. dollars at the exchange rates prevailing at the end of the period.
Purchases and sales of investments and items of income and expense are
translated on the respective dates of such transactions.





NOTES TO PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2016 (UNAUDITED)


                           3. DERIVATIVE TRANSACTIONS

Written options activity for the Fund for the fiscal year-to-date period
(December 1, 2015 through August 31, 2016) was as follows:

                                                  NUMBER OF
WRITTEN OPTIONS                                   CONTRACTS       PREMIUMS
----------------------------------------------------------------------------
Options outstanding at November 30,2015 .......       25,130   $   1,352,376
Options Written................................      103,240       5,514,523
Options Expired................................      (49,666)     (2,436,618)
Options Exercised..............................      (28,355)     (1,646,708)
Options Closed.................................      (18,089)     (1,038,493)
                                                 -----------   -------------
Options outstanding at August 31, 2016.........       32,260   $   1,745,080
                                                 ===========   =============

The average volume of interest rate swaps was $72,950,000 for the fiscal
year-to-date period (December 1, 2015 through August 31, 2016).





ITEM 2. CONTROLS AND PROCEDURES.

   (a) The registrant's principal executive and principal financial officers, or
       persons performing similar functions, have concluded that the
       registrant's disclosure controls and procedures (as defined in Rule
       30a-3(c) under the Investment Company Act of 1940, as amended (the "1940
       Act") (17 CFR 270.30a-3(c))) are effective, as of a date within 90 days
       of the filing date of the report that includes the disclosure required by
       this paragraph, based on their evaluation of these controls and
       procedures required by Rule 30a-3(b) under the 1940 Act (17 CFR
       270.30a-3(b)) and Rules 13a-15(b) or 15d-15(b) under the Securities
       Exchange Act of 1934, as amended (17 CFR 240.13a-15(b) or 240.15d-15(b)).

   (b) There were no changes in the registrant's internal control over financial
       reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR
       270.30a-3(d)) that occurred during the registrant's last fiscal quarter
       that have materially affected, or are reasonably likely to materially
       affect, the registrant's internal control over financial reporting.

ITEM 3. EXHIBITS.

Certifications pursuant to Rule 30a-2(a) under the 1940 Act and Section 302 of
the Sarbanes-Oxley Act of 2002 are attached hereto.


                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant)        First Trust Energy Infrastructure Fund
              ---------------------------------------------------

By (Signature and Title)*               /s/ James M. Dykas
                                        ----------------------------------------
                                        James M. Dykas
                                        President and Chief Executive Officer
                                        (principal executive officer)

Date: October 20, 2016
     ------------------

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.

By (Signature and Title)*               /s/ James M. Dykas
                                        ----------------------------------------
                                        James M. Dykas
                                        President and Chief Executive Officer
                                        (principal executive officer)

Date: October 20, 2016
     ------------------

By (Signature and Title)*               /s/ Donald P. Swade
                                        ----------------------------------------
                                        Donald P. Swade
                                        Treasurer, Chief Financial Officer and
                                        Chief Accounting Officer
                                        (principal financial officer)

Date: October 20, 2016
     ------------------


*Print the name and title of each signing officer under his or her signature.