As filed with the Securities and Exchange Commission on September 27, 2011
================================================================================
                                                    1933 Act File No. 333-______
                                                     1940 Act File No. 811-22528


                    U.S. SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                    FORM N-2

(Check appropriate box or boxes)


[X]  REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933
[ ]  Pre-Effective Amendment No. _
[ ]  Post-Effective Amendment No. _

and

[ ]  REGISTRATION STATEMENT UNDER THE INVESTMENT COMPANY ACT OF 1940
[X]  Amendment No. 4


                     First Trust Energy Infrastructure Fund
         Exact Name of Registrant as Specified in Declaration of Trust

           120 East Liberty Drive, Suite 400, Wheaton, Illinois 60187
 Address of Principal Executive Offices (Number, Street, City, State, Zip Code)

                                 (630) 765-8000
               Registrant's Telephone Number, including Area Code


                             W. Scott Jardine, Esq.
                          First Trust Portfolios L.P.
                       120 East Liberty Drive, Suite 400
                            Wheaton, Illinois 60187

 Name and Address (Number, Street, City, State, Zip Code) of Agent for Service


                          Copies of Communications to:

           Eric F. Fess, Esq.                 Sarah E. Cogan, Esq.
         Chapman and Cutler LLP         Simpson Thacher & Bartlett LLP
         111 West Monroe Street              425 Lexington Avenue
         Chicago, Illinois 60603           New York, New York 10017





Approximate Date of Proposed Public Offering: As soon as practicable after the
effective date of this Registration Statement

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

If any of the securities being registered on this form are offered on a delayed
or continuous basis in reliance on Rule 415 under the Securities Act of 1933,
other than securities offered in connection with a dividend reinvestment plan,
check the following box. [ ]

It is proposed that this filing will become effective (check appropriate box)

     [ ] when declared effective pursuant to section 8(c)


If appropriate, check the following box:

     [ ] This post-effective amendment designates a new effective date for a
         previously filed registration statement.

     [X] This form is filed to register additional securities for an offering
         pursuant to Rule 462(b) under the Securities Act and the Securities
         Act registration statement number of the earlier effective registration
         statement for the same offering is 333-172439.

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



CALCULATION OF REGISTRATION FEE UNDER THE SECURITIES ACT OF 1933
================================================================================

------------------------ ---------------------- --------------------- ---------------------- ---------------------
                                                  Proposed Maximum       Proposed Maximum
  Title of Securities         Amount Being         Offering Price       Aggregate Offering         Amount of
    Being Registered           Registered(1)          Per Unit               Price(2)           Registration Fee
------------------------ ---------------------- --------------------- ---------------------- ---------------------
                                                                                      
 Common Shares, $0.01
       par value                2,265,000             $20.00               $45,300,000            $5,259.33
------------------------ ---------------------- --------------------- ---------------------- ---------------------


(1)   All of which may be purchased pursuant to an over-allotment option of
      2,518,115 shares granted by the Registrant to the Underwriters.

(2)   Estimated solely for the purpose of determining the registration fee.


================================================================================






                EXPLANATORY NOTE AND INCORPORATION BY REFERENCE

       This Registration Statement is being filed pursuant to Rule 462(b) under
the Securities Act of 1933, as amended. The contents of the Registration
Statement on Form N-2 (Reg. No. 333-172439) filed by First Trust Energy
Infrastructure Fund (the "Registrant") with the Securities and Exchange
Commission, declared effective September 27, 2011, are incorporated herein by
reference. On September 27, 2011, the Registrant registered 17,500,000 common
shares in Pre-Effective Amendment No. 3 to the Registrant's Registration
Statement filed on Form N-2. When the common shares previously registered are
combined with the common shares registered herein, the total number of shares
registered by the Registrant is 19,765,000 shares. Any required consents are
listed on an Exhibit Index attached hereto and are filed herewith.







                           PART C - OTHER INFORMATION

Item 25: Financial Statements and Exhibits

1.    Financial Statements:

      Registrant has not conducted any business as of the date of this filing,
other than in connection with its organization. Financial Statements indicating
that the Registrant has met the net worth requirements of Section 14(a) of the
Investment Company Act of 1940 were filed with Pre-effective Amendment No. 2 to
the Registration Statement on Form N-2 (File No. 333-172439).

2.    Exhibits:

a.    Declaration of Trust dated February 22, 2011. (1)

b.    By-Laws of Fund. (2)

c.    None.

d.    None.

e.    Terms and Conditions of the Dividend Reinvestment Plan. (3)

f.    None.

g.1   Form of Investment Management Agreement between Registrant and First Trust
      Advisors L.P. (3)

g.2   Form of Sub-Advisory Agreement between Registrant, First Trust Advisors
      L.P. and Energy Income Partners, LLC. (3)

h.1   Form of Underwriting Agreement. (3)

h.2   Form of Master Agreement Among Underwriters. (3)

h.3   Form of Master Selected Dealers Agreement. (3)

i.    None.

j.    Form of Custodian Services Agreement between Registrant and Fund
      Custodian. (3)

k.1   Form of Transfer Agency Services Agreement between Registrant and Fund
      Transfer Agent. (3)

k.2   Form of Administration and Accounting Services Agreement. (3)

k.3   Form of Structuring Fee Agreement with Morgan Stanley & Co. LLC. (3)





k.4   Form of Syndication Fee Agreement with Morgan Stanley & Co. LLC. (3)

k.5   Form of Structuring Fee Agreement with Citigroup Global Markets Inc. (3)

k.6   Form of Structuring Fee Agreement with Merrill Lynch, Pierce, Fenner &
      Smith Incorporated. (3)

k.7   Form of Structuring Fee Agreement with RBC Capital Markets, LLC. (3)

l.1   Opinion and consent of Chapman and Cutler LLP. (4)

l.2   Opinion and consent of Bingham McCutchen LLP. (4)

m.    None.

n.    Consent of Independent Registered Public Accounting Firm. (4)

o.    None.

p.    Subscription Agreement between Registrant and First Trust Advisors L.P.
      (3)

q.    None.

r.1   Code of Ethics of Registrant. (3)

r.2   Code of Ethics of First Trust Portfolios L.P. (3)

r.3   Code of Ethics of First Trust Advisors L.P. (3)

r.4.  Code of Ethics of Energy Income Partners, LLC. (3)

s.    Powers of Attorney. (2)

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

(1)  Filed on February 25, 2011 as Exhibit a. to Registrant's Registration
     Statement on Form N-2 (File No. 333-172439) and incorporated herein by
     reference.

(2)  Filed on July 20, 2011 in Pre-Effective Amendment No. 1 to Registrant's
     Registration Statement on Form N-2 (File No. 333-172439) and incorporated
     herein by reference.

(3)  Filed on September 27, 2011 in Pre-Effective Amendment No. 3 to
     Registrant's Registration Statement on Form N-2 (File No. 333-172439) and
     incorporated herein by reference.

(4)  Filed herewith.

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





Item 26: Marketing Arrangements

      See the Form of Underwriting Agreement, the Form of Master Agreement Among
Underwriters, the Form of Master Selected Dealers Agreement, the Form of
Structuring Fee Agreement of Morgan Stanley & Co. LLC, the Form of Syndication
Fee Agreement of Morgan Stanley & Co. LLC, the Form of Structuring Fee Agreement
of Citigroup Global Markets Inc., the Form of Structuring Fee Agreement of
Merrill Lynch, Pierce, Fenner & Smith Incorporated and the Form of Structuring
Fee Agreement of RBC Capital Markets, LLC, filed as Exhibit (h)(1), Exhibit
(h)(2), Exhibit (h)(3), Exhibit (k)(3), Exhibit (k)(4), Exhibit (k)(5), Exhibit
(k)(6) and Exhibit (k)(7), respectively, to Registrant's Registration Statement
filed on Form N-2 (File No. 333-172439).






Item 27:  Other Expenses of Issuance and Distribution

---------------------------------------------------------- --------------------
Securities and Exchange Commission Fees                    $ 40,055
---------------------------------------------------------- --------------------
Financial Industry Regulatory Authority, Inc. Fees         $ 40,500
---------------------------------------------------------- --------------------
Printing and Engraving Expenses                            $150,000
---------------------------------------------------------- --------------------
Legal Fees                                                 $388,445
---------------------------------------------------------- --------------------
Listing Fees                                               $ 30,000
---------------------------------------------------------- --------------------
Accounting Expenses                                        $ 16,000
---------------------------------------------------------- --------------------
Blue Sky Filing Fees and Expenses                          $     --
---------------------------------------------------------- --------------------
Miscellaneous Expenses                                     $ 25,000
---------------------------------------------------------- --------------------
Total                                                      $690,000
---------------------------------------------------------- --------------------


Item 28: Persons Controlled by or under Common Control with Registrant

    Not applicable.


Item 29:  Number of Holders of Securities

    At September 27, 2011

----------------------------------------------------- --------------------------
Title of Class                                        Number of Record Holders
----------------------------------------------------- --------------------------
Common Shares, $0.01 par value                        1
----------------------------------------------------- --------------------------





Item 30: Indemnification

Section 9.5 of the Registrant's Declaration of Trust provides as follows:

      Indemnification and Advancement of Expenses. Subject to the exceptions and
limitations contained in this Section 9.5, every person who is, or has been, a
Trustee, officer or employee of the Trust, including persons who serve at the
request of the Trust as directors, trustees, officers, employees or agents of
another organization in which the Trust has an interest as a shareholder,
creditor or otherwise (hereinafter referred to as a "Covered Person"), shall be
indemnified by the Trust to the fullest extent permitted by law against
liability and against all expenses reasonably incurred or paid by him in
connection with any claim, action, suit or proceeding in which he becomes
involved as a party or otherwise by virtue of his being or having been such a
Trustee, director, officer, employee or agent and against amounts paid or
incurred by him in settlement thereof.

      No indemnification shall be provided hereunder to a Covered Person to the
extent such indemnification is prohibited by applicable federal law.

      The rights of indemnification herein provided may be insured against by
policies maintained by the Trust, shall be severable, shall not affect any other
rights to which any Covered Person may now or hereafter be entitled, shall
continue as to a person who has ceased to be such a Covered Person and shall
inure to the benefit of the heirs, executors and administrators of such a
person.

      Subject to applicable federal law, expenses of preparation and
presentation of a defense to any claim, action, suit or proceeding subject to a
claim for indemnification under this Section 9.5 shall be advanced by the Trust
prior to final disposition thereof upon receipt of an undertaking by or on
behalf of the recipient to repay such amount if it is ultimately determined that
he is not entitled to indemnification under this Section 9.5.

      To the extent that any determination is required to be made as to whether
a Covered Person engaged in conduct for which indemnification is not provided as
described herein, or as to whether there is reason to believe that a Covered
Person ultimately will be found entitled to indemnification, the Person or
Persons making the determination shall afford the Covered Person a rebuttable
presumption that the Covered Person has not engaged in such conduct and that
there is reason to believe that the Covered Person ultimately will be found
entitled to indemnification.

      As used in this Section 9.5, the words "claim," "action," "suit" or
"proceeding" shall apply to all claims, demands, actions, suits, investigations,
regulatory inquiries, proceedings or any other occurrence of a similar nature,
whether actual or threatened and whether civil, criminal, administrative or
other, including appeals, and the words "liability" and "expenses" shall include
without limitation, attorneys' fees, costs, judgments, amounts paid in
settlement, fines, penalties and other liabilities.

      Section 8 of the Form of Underwriting Agreement filed as Exhibit (h)(1) to
this Registration Statement provides for each of the parties thereto, including
the Registrant and the underwriters, to indemnify the others, their directors,
officers, agents, affiliates and persons who control them against certain





liabilities in connection with the offering described herein, including
liabilities under the federal securities laws.


Item 31: Business and Other Connections of Investment Advisers

      (a) First Trust Advisors L.P. ("First Trust Advisors") serves as
investment advisor to the Registrant and the First Defined Portfolio Fund, LLC
and also serves as advisor or sub-advisor to 20 mutual funds, four
exchange-traded funds consisting of 44 series and 14 other closed-end funds and
is the portfolio supervisor of certain unit investment trusts. Its principal
address is 120 East Liberty Drive, Suite 400, Wheaton, Illinois 60187.

The principal business of certain of First Trust Advisors' principal executive
officers involves various activities in connection with the family of unit
investment trusts sponsored by First Trust Portfolios L.P. ("First Trust
Portfolios" or "FTP"). The principal address of First Trust Portfolios is 120
East Liberty Drive, Suite 400, Wheaton, Illinois 60187.

Information as to Other Business, Profession, Vocation or Employment During Past
Two Years of the Officers and Directors of First Trust Advisors is as follows:

NAME AND POSITION WITH FIRST TRUST      EMPLOYMENT DURING PAST TWO YEARS

James A. Bowen, Managing Director/      Managing Director/Chief Executive
Chief Executive Officer                 Officer (December 2010 to Present),
                                        Managing Director/President (prior to
                                        and including December 2008 to December
                                        2010), FTP; Chairman of the Board of
                                        Directors, BondWave LLC and Stonebridge
                                        Advisors LLC

Ronald D. McAlister, Managing Director  Managing Director, FTP

Mark R. Bradley, Chief Financial        Chief Financial Officer, Chief Operating
Officer, Chief Operations Officer and   Officer and Managing Director (December
Managing Director                       2010 to Present), Managing Director
                                        (prior to and including December 2008 to
                                        December 2010), FTP; Chief Financial
                                        Officer, BondWave LLC and Stonebridge
                                        Advisors LLC

Robert F. Carey, Chief Investment       Senior Vice President, FTP
Officer and Senior Vice President

W. Scott Jardine, General Counsel       General Counsel, FTP and BondWave LLC;
                                        Secretary of Stonebridge Advisors LLC

Kristi A. Maher, Deputy General         Deputy General Counsel, FTP
Counsel

Erin Chapman, Assistant General         Assistant General Counsel, FTP
Counsel

John Vasko, Assistant General Counsel   Assistant General Counsel, FTP





NAME AND POSITION WITH FIRST TRUST      EMPLOYMENT DURING PAST TWO YEARS

Amy Lum, Assistant General Counsel      Assistant General Counsel, FTP since
                                        November 2010; Of Counsel, The Law
                                        Offices of Beau T. Greiman, August 2009
                                        to March 2010; Associate, Perkins Coie,
                                        April 2008 to August 2009

Lisa Weier, Assistant General Counsel   Assistant General Counsel (since January
                                        2011), FTP; Associate, Chapman and
                                        Cutler LLP

R. Scott Hall, Managing Director        Managing Director, FTP

Andrew S. Roggensack, Managing          Managing Director/President (December
Director/President                      2010 to Present), Managing Director
                                        (prior to and including December 2008
                                        to December 2010), FTP

Kathleen Brown, Senior Vice President   Senior Vice President and CCO
and Chief Compliance Officer


Elizabeth H. Bull, Senior Vice          Senior Vice President, FTP
President

Christopher L. Dixon, Senior Vice       Senior Vice President, FTP
President

Jane Doyle, Senior Vice President       Senior Vice President, FTP

James M. Dykas, Senior Vice President   Senior Vice President, FTP

Jon C. Erickson, Senior Vice President  Senior Vice President, FTP

Ken Fincher, Senior Vice President      Senior Vice President, FTP

Kenneth N. Hass, Senior Vice President  Senior Vice President, FTP

Jason T. Henry, Senior Vice President   Senior Vice President, FTP

Daniel J. Lindquist, Senior Vice        Senior Vice President, FTP
President

David G. McGarel, Senior Vice           Senior Vice President, FTP
President

Mitchell Mohr, Senior Vice President    Senior Vice President, FTP

Robert M. Porcellino, Senior Vice       Senior Vice President, FTP
President

Alan M. Rooney, Senior Vice President   Senior Vice President, FTP

Roger F. Testin, Senior Vice President  Senior Vice President, FTP

Kyle Baker, Vice President              Vice President, FTP

Christina Knierim, Vice President       Vice President, FTP

Todd Larson, Vice President             Vice President, FTP





NAME AND POSITION WITH FIRST TRUST      EMPLOYMENT DURING PAST TWO YEARS

Ronda L. Saeli-Chiappe, Vice President  Vice President, FTP

Stan Ueland, Vice President             Vice President, FTP

Katherine Urevig, Vice President        Vice President, FTP

Brad Bradley, Assistant Vice President  Assistant Vice President, FTP

Katie D. Collins, Assistant Vice        Assistant Vice President, FTP
President

Chris Fallow, Assistant Vice President  Assistant Vice President, FTP

Kristen Johanneson, Assistant Vice      Assistant Vice President, FTP
President

Coleen D. Lynch, Assistant Vice         Assistant Vice President, FTP
President

Omar Sepulveda, Assistant Vice          Assistant Vice President, FTP
President

John H. Sherren, Assistant Vice         Assistant Vice President, FTP
President

Brian Wesbury, Chief Economist          Chief Economist, FTP

Rob Stein, Senior Economist             Senior Economist, FTP


      (b) Sub-Advisor. Energy Income Partners, LLC serves as an investment
sub-advisor of the Fund. Reference is made to: (i) the information set forth
under "Management of the Fund" in the Prospectus and "Sub-Advisor" in the
Statement of Additional Information; and (ii) the Form ADV of Energy Income
Partners, LLC (File No. 801-66907) filed with the Commission, all of which are
incorporated herein by reference.


Item 32: Location of Accounts and Records.

First Trust Advisors L.P. maintains the Declaration of Trust, By-Laws, minutes
of trustees and shareholders meetings and contracts of the Registrant, all
advisory material of the investment adviser, all general and subsidiary ledgers,
journals, trial balances, records of all portfolio purchases and sales, and all
other required records.


Item 33: Management Services

Not applicable.


Item 34: Undertakings

1.    Registrant undertakes to suspend the offering of its shares until it
      amends its prospectus if (1) subsequent to the effective date of its
      Registration Statement, the net asset value declines more than 10 percent
      from its net asset value as of the effective date of the Registration





      Statement, or (2) the net asset value increases to an amount greater than
      its net proceeds as stated in the prospectus.

2.    Not applicable.


3.    Not applicable.


4.    Not applicable.


5.    The Registrant undertakes that:

a.    For purposes of determining any liability under the Securities Act of
      1933, the information omitted from the form of prospectus filed as part of
      a registration statement in reliance upon Rule 430A and contained in the
      form of prospectus filed by the Registrant under Rule 497(h) under the
      Securities Act of 1933 shall be deemed to be part of the Registration
      Statement as of the time it was declared effective; and

b.    For the purpose of determining any liability under the Securities Act of
      1933, each post-effective amendment that contains a form of prospectus
      shall be deemed to be a new registration statement relating to the
      securities offered therein, and the offering of the securities at that
      time shall be deemed to be the initial bona fide offering thereof.


6.    The Registrant undertakes to send by first class mail or other means
      designed to ensure equally prompt delivery, within two business days of
      receipt of a written or oral request, any Statement of Additional
      Information.






                                   SIGNATURES

      Pursuant to the requirements of the Securities Act of 1933 and the
Investment Company Act of 1940, the Registrant has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in this City of Wheaton, and State of Illinois, on the 27th day of
September, 2011.

                                          FIRST TRUST ENERGY INFRASTRUCTURE FUND



                                          By:        /s/ James A. Bowen
                                             -----------------------------------
                                                 James A. Bowen, President

      Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below by the following persons in the
capacities and on the date indicated.



------------------------------------------------------------------------------------------------------------------
                                                                        
Signature                               Title                                 Date
------------------------------------------------------------------------------------------------------------------
/s/ James A. Bowen                      President, Chairman of the Board      September 27, 2011
-------------------------------------   and Trustee (Principal Executive
 James A. Bowen                         Officer)
------------------------------------------------------------------------------------------------------------------
/s/ Mark R. Bradley                     Chief Financial Officer and           September 27, 2011
-------------------------------------   Treasurer (Principal Financial and
 Mark R. Bradley                        Accounting Officer)
------------------------------------------------------------------------------------------------------------------
Richard E. Erickson(1)                  Trustee                            )  By:     /s/ W. Scott Jardine
-------------------------------------   -----------------------------------)     ---------------------------------
Thomas R. Kadlec(1)                     Trustee                            )           W. Scott Jardine
-------------------------------------   -----------------------------------)           Attorney-In-Fact
Robert F. Keith(1)                      Trustee                            )           September 27, 2011
-------------------------------------   -----------------------------------)
Niel B. Nielson(1)                      Trustee                            )
------------------------------------------------------------------------------------------------------------------


(1) Original powers of attorney authorizing James A. Bowen, W. Scott Jardine,
Mark R. Bradley, Kristi A. Maher and Eric F. Fess to execute Registrant's
Registration Statement, and Amendments thereto, for each of the trustees of the
Registrant on whose behalf this Pre-Effective Amendment No. 3 is filed, were
previously executed and are filed as Exhibit s. to the Registrant's Registration
Statement on Form N-2 (File No. 333-172439).






                               INDEX TO EXHIBITS


l.1   Opinion and consent of Chapman and Cutler LLP.

l.2   Opinion and consent of Bingham McCutchen LLP.

n.    Consent of Independent Registered Public Accounting Firm.