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

                                  SCHEDULE 13D
                                 (Rule 13d-101)
                               (Amendment No. 13)


             INFORMATION TO BE INCLUDED IN STATEMENTS FILED PURSUANT
            TO RULE 13d-1(a) AND AMENDMENTS THERETO FILED PURSUANT TO
                                  RULE 13d-2(a)


                              The Korea Fund, Inc.
                                (Name of Issuer)

                     Common Stock, par value $.01 per share
                         (Title of Class of Securities)

                                    500634100
                                 (CUSIP Number)

                                 Barry M. Olliff
            c/o City of London Investment Management Company Limited
                     10 Eastcheap, London EC3M ILX, England
                                +44 207 711 0771
           (Name, Address and Telephone Number of Person Authorized to
                       Receive Notices and Communications)

                                 October 7, 2005
             (Date of Event Which Requires Filing of This Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(e), (f) or (g), check the following box / /.

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 or otherwise subject to the liabilities of that section of the Act but
shall be subject to all other provisions of the Act.
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                                   Page 1 of 6


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     1     NAME OF REPORTING PERSONS
           S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS

           City of London Investment Group PLC, a company incorporated under
           the laws of England and Wales.
---------- ---------------------------------------------------------------------
     2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP              (A) |_|
                                                                         (B) |_|

---------- ---------------------------------------------------------------------
     3     SEC USE ONLY


---------- ---------------------------------------------------------------------
     4     SOURCE OF FUNDS*

           OO
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     5     CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
           TO ITEM 2(D) OR 2(E)
                                                                             |_|
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     6     CITIZENSHIP OR PLACE OF ORGANIZATION

           England and Wales
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      NUMBER OF           7    SOLE VOTING POWER

        SHARES                 5,440,119
                        ------ -------------------------------------------------
     BENEFICIALLY         8    SHARED VOTING POWER                              
                                                                                
       OWNED BY                0                                                
                        ------ -------------------------------------------------
         EACH             9    SOLE DISPOSITIVE POWER                           
                                                                                
      REPORTING                5,440,119                                        
                        ------ -------------------------------------------------
        PERSON           10    SHARED DISPOSITIVE POWER                         
                                                                                
         WITH                  0                                                

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    11     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           5,440,119
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    12     CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
           |_|

---------- ---------------------------------------------------------------------
    13     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

           18.15%
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    14     TYPE OF REPORTING PERSON*

           HC
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                                   Page 2 of 6


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     1     NAME OF REPORTING PERSONS
           S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS

           City of London Investment Management Company Limited, a company
           incorporated under the laws of England and Wales.
---------- ---------------------------------------------------------------------
     2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP              (A) |_|
                                                                         (B) |_|

---------- ---------------------------------------------------------------------
     3     SEC USE ONLY


---------- ---------------------------------------------------------------------
     4     SOURCE OF FUNDS

           WC
---------- ---------------------------------------------------------------------
     5     CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO 
           ITEMS 2(D) OR 2(E)
                                                                             |_|

---------- ---------------------------------------------------------------------
     6     CITIZENSHIP OR PLACE OF ORGANIZATION

           England and Wales

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      NUMBER OF           7    SOLE VOTING POWER

        SHARES                 5,440,119
                        ------ -------------------------------------------------
     BENEFICIALLY         8    SHARED VOTING POWER                              
                                                                                
       OWNED BY                0                                                
                        ------ -------------------------------------------------
         EACH             9    SOLE DISPOSITIVE POWER                           
                                                                                
      REPORTING                5,440,119                                        
                        ------ -------------------------------------------------
        PERSON           10    SHARED DISPOSITIVE POWER                         
                                                                                
         WITH                  0                                                

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    11     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           5,440,119
---------- ---------------------------------------------------------------------
    12     CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
           |_|

---------- ---------------------------------------------------------------------
    13     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

           18.15%
---------- ---------------------------------------------------------------------
    14     TYPE OF REPORTING PERSON*

           IA
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                                   Page 3 of 6


This Amendment No. 13 to Schedule 13D (this "Amendment No. 13") should be read
in conjunction with the Schedule 13D filed with the U.S. Securities and Exchange
Commission (the "SEC") on February 17, 2004 (the "Original Schedule 13D"), with
Amendment No. 1 to Schedule 13D filed with the SEC on March 1, 2004 ("Amendment
No. 1"), with Amendment No. 2 to Schedule 13D filed with the SEC on May 5, 2004
("Amendment No. 2"), with Amendment No. 3 to Schedule 13D filed with the SEC on
July 8, 2004 ("Amendment No. 3"), with Amendment No. 4 to Schedule 13D filed
with the SEC on August 31, 2004 ("Amendment No. 4"), with Amendment No. 5 to
Schedule 13D filed with the SEC on November 15, 2004 ("Amendment No. 5"), with
Amendment No. 6 to Schedule 13D filed with the SEC on December 23, 2004
("Amendment No. 6"), with Amendment No. 7 to Schedule 13D filed with the SEC on
May 18, 2005 ("Amendment No. 7"), with Amendment No. 8 to Schedule 13D filed
with the SEC on June 10, 2005 ("Amendment No. 8"), with Amendment No. 9 to
Schedule 13D filed with the SEC on July 5, 2005 ("Amendment No. 9"), with
Amendment No. 10 to Schedule 13D filed with the SEC on August 5, 2005
("Amendment No. 10"), and with Amendment No. 11 to Schedule 13D filed with the
SEC on August 12, 2005 ("Amendment No. 11"), and with Amendment No. 12 to
Schedule 13D filed with the SEC on September 14, 2005 ("Amendment No. 12") and,
together with Amendment No. 1, Amendment No. 2, Amendment No. 3, Amendment No.
4, Amendment No. 5, Amendment No. 6, Amendment No. 7, Amendment No. 8, Amendment
No. 9. Amendment No. 10, Amendment No. 11, and Amendment No. 12, the
"Amendments") by City of London Investment Group PLC ("City of London") and City
of London Investment Management Company Limited relating to the shares of common
stock, par value $0.01 per share (the "Shares"), of The Korea Fund, Inc., a
Maryland corporation (the "Fund"). This Amendment No. 13 amends Items 4 and 7 of
the Original Schedule 13D as amended by the Amendments. All other information in
the Original Schedule 13D and the Amendments remains in effect. All capitalized
terms used herein and not otherwise defined shall have the meanings ascribed
thereto in the Original Schedule 13D as amended by the Amendments.

ITEM 4.   PURPOSE OF TRANSACTION.

          Item 4 is hereby amended by adding the following:

          On October 7, 2005, CLIG sent a letter to the Chairman of the
          Board of Directors of the Korea Fund Inc. In the letter, CLIG
          requests the Chairman of the Board of Directors to address
          certain concerns relating to corporate governance surrounding
          the upcoming AGM. The foregoing description of the letter is
          not intended to be complete and it is qualified in its entirety
          by the complete text of the letter, which is filed as Exhibit A
          hereto and is incorporated herein by reference.

          The Reporting Persons reserve the right to acquire, or cause to
          be acquired, additional securities of the Fund, to dispose of,
          or cause to be disposed, such securities at any time or to
          formulate other purposes, plans or proposals regarding the Fund
          or any of its securities, to the extent deemed advisable in
          light of general investment and trading policies of the
          Reporting Persons, market conditions or other factors.

                                   Page 4 of 6


          Other than as set forth above, none of the Reporting Persons
          or, in the case of non- individual Reporting Persons, any of
          their directors or executive officers identified in Item 2,
          have any present plans or proposals which relate to or could
          result in, any of the matters referred to in paragraphs (a)
          through (j), inclusive, of Item 4 of Schedule 13D (although
          they reserve the right to develop any such plans or proposals).


ITEM 7    MATERIALS TO BE FILED AS EXHIBITS

          Item 7 is hereby amended by adding the following:

          Exhibit A.   Letter sent to the Chairman of the Board of Directors 
                       dated October 7, 2005





















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                                    SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this statement is true, complete and correct.

Dated: October 7, 2005


                                           CITY OF LONDON INVESTMENT GROUP PLC


                                           /s/ Barry M. Olliff   
                                           -----------------------------        
                                           Name: Barry M. Olliff
                                           Title: Director


                                           CITY OF LONDON INVESTMENT 
                                           MANAGEMENT COMPANY LIMITED


                                           /s/ Barry M. Olliff  
                                           -----------------------------        
                                           Name: Barry M. Olliff
                                           Title: Director










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