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

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


                                  SCHEDULE 13D
                                 (Rule 13d-101)
                                (Amendment No. 6)


             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)


                                December 23, 2004
             -------------------------------------------------------
             (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.

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

                               (Page 1 of 7 Pages)

===================                                                  ===========
CUSIP NO. 500634100                    13D                           PAGE 2 of 7
===================                                                  ===========

================================================================================
     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
------------ -------------------------------------------------------------------
     5       CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT
             TO ITEM 2(d) OR 2(e)
                                                                             [_]
------------ -------------------------------------------------------------------
     6       CITIZENSHIP OR PLACE OF ORGANIZATION

             England and Wales
--------------------------------------------------------------------------------
  NUMBER OF              7      SOLE VOTING POWER

   SHARES                       4,441,782
                   ------------ ------------------------------------------------
BENEFICIALLY             8      SHARED VOTING POWER

  OWNED BY                      0
                   ------------ ------------------------------------------------
    EACH                 9      SOLE DISPOSITIVE POWER

  REPORTING                     4,441,782
                   ------------ ------------------------------------------------
   PERSON               10      SHARED DISPOSITIVE POWER

    WITH                        0
------------ -------------------------------------------------------------------
    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

             4,441,782
------------ -------------------------------------------------------------------
    12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN
             SHARES
                                                                             [_]
------------ -------------------------------------------------------------------
    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

             9.94%
------------ -------------------------------------------------------------------
    14       TYPE OF REPORTING PERSON*

             HC
================================================================================

                               (Page 2 of 7 Pages)

===================                                                  ===========
CUSIP NO. 500634100                    13D                           PAGE 3 of 7
===================                                                  ===========

================================================================================
     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 ITEM 2(d) OR 2(e)
                                                                             [_]
------------ -------------------------------------------------------------------
     6       CITIZENSHIP OR PLACE OF ORGANIZATION

             England and Wales
--------------------------------------------------------------------------------
  NUMBER OF              7      SOLE VOTING POWER

   SHARES                       4,413,762
                   ------------ ------------------------------------------------
BENEFICIALLY             8      SHARED VOTING POWER

  OWNED BY                      0
                   ------------ ------------------------------------------------
    EACH                 9      SOLE DISPOSITIVE POWER

  REPORTING                     4,413,762
                   ------------ ------------------------------------------------
   PERSON               10      SHARED DISPOSITIVE POWER

    WITH                        0
------------ -------------------------------------------------------------------
    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

             4,413,762
------------ -------------------------------------------------------------------
    12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN
             SHARES
                                                                             [_]
------------ -------------------------------------------------------------------
    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

             9.87%
------------ -------------------------------------------------------------------
    14       TYPE OF REPORTING PERSON*

             IA
================================================================================

                               (Page 3 of 7 Pages)


This Amendment No. 6 to Schedule 13D (this "Amendment No. 6") 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") and with Amendment No. 5 to
Schedule 13D filed with the SEC on November 15, 2004 ("Amendment No. 5" and,
together with Amendment No. 1, Amendment No. 2, Amendment No. 3 and Amendment
No. 4, 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. 6
amends Items 3, 4, 5 and 7 of the Original Schedule 13D as amended by the
Amendments. All other information in the Original Schedule 13D and the
Amendments remain 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 3.    SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.
           --------------------------------------------------

           Item 3 is hereby amended and restated in its entirety to read as
           follows:

           The funds used to purchase the Shares described in this statement
           were acquired through open market purchases and were derived from
           EWF's, GEM's, IEM's, GFM's, FREE's and Global's investment capital
           and funds provided by the Accounts. The aggregate amount of the funds
           used to purchase all of the Shares purchased by EWF, GEM, IEM, GFM,
           FREE, Global's and the Accounts is $1,933,746, $18,788,073,
           $18,090,202, $1,933,266, $6,587,458, $489,912, and $31,933,884,
           respectively.


ITEM 4.    PURPOSE OF TRANSACTION.
           -----------------------

           Item 4 is hereby amended by adding the following:

           On December 23, 2004, CLIG sent a letter to the Board of Directors of
           the Fund. In the letter, CLIG responds to the measures approved by
           the Board of Directors of the Fund and described in the Fund's
           December 15, 2004 press release. 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.

           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).

                               (Page 4 of 7 Pages)


ITEM 5.    INTERESTS IN SECURITIES OF THE ISSUER.
           --------------------------------------

           Items 5(a) and 5(b) below are hereby amended and restated in their
           entirety and Item 5(c) is hereby amended as follows:

           (a) and (b). As of the date hereof, EWF, GEM, IEM, GFM, FREE, the
           Accounts and Global owned directly 132,036, 1,157,847, 1,118,627,
           118,436, 322,994, 1,553,822 and 28,020 Shares, respectively,
           representing approximately 0.30%, 2.59%, 2.50%, 0.26%, 0.74%, 3.47%
           and 0.06%, respectively, of the Shares outstanding (based on the most
           recent Share information publicly disclosed by the Fund).

           As of the date hereof, CLIG, through its control of CLIM and City of
           London Quantitative Management Ltd., is the beneficial owner of
           4,441,782 Shares, representing approximately 9.94% of the Shares
           outstanding (based on the most recent Share information publicly
           disclosed by the Fund).

           As of the date hereof, CLIM, through EWF, GEM, IEM, FREE, GFM and the
           Accounts, is the beneficial owner of 4,413,762 Shares, representing
           approximately 9.87% of the Shares outstanding (based on the most
           recent Share information publicly disclosed by the Fund).

           (c). Except as described below, no transactions in the Shares were
           effected by the Reporting Persons, or, to their knowledge, any of the
           persons identified in Item 2, since the filing of Amendment No. 5.

           Since the filing of Amendment No. 5, the following open market
           purchases of Shares have been made by FREE:

           Date of Purchase
           Number of Shares Purchased
           Price Paid/Share

           November 15, 2004
           10,000
           $22.0600

           Since the filing of Amendment No. 5, the following open market
           purchases of Shares have been made by GFM:

           Date of Purchase
           Number of Shares Purchased
           Price Paid/Share


                               (Page 5 of 7 Pages)


           November 15, 2004
           5,000
           $22.0600


ITEM 7.    MATERIALS TO BE FILED AS EXHIBITS.
           ----------------------------------

           Item 7 is hereby amended by adding the following:

           Exhibit A. Letter, dated December 23, 2004, from City of London to
           the Chairman of the Board of Directors of the Fund.


















                               (Page 6 of 7 Pages)


                                    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:     December 23, 2004


                                            CITY OF LONDON INVESTMENT GROUP PLC



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







                                            CITY OF LONDON INVESTMENT 
                                            MANAGEMENT COMPANY LIMITED



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







                               (Page 7 of 7 Pages)