SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 6-K

      Report of Foreign Private Issuer Pursuant to Rule 13a-16 or 15d-16 of
                       The Securities Exchange Act of 1934

                        For the month of September, 2010

                                   TEFRON LTD.
                 (Translation of registrant's name into English)

            IND. CENTER TERADYON, P.O. BOX 1365, MISGAV 20179, ISRAEL
                    (Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports
under cover Form 20-F or Form 40-F.

                         Form 20-F [X]     Form 40-F [_]

Indicate by check mark if the registrant is submitting the Form 6-K in paper as
permitted by Regulation S-T Rule 101(b)(1): ____

Indicate by check mark if the registrant is submitting the Form 6-K in paper as
permitted by Regulation S-T Rule 101(b)(7): ____

Indicate by check mark whether the registrant by furnishing the information
contained in this form is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                               Yes [_]     No [X]

If "Yes" is marked, indicate below the file number assigned to the registrant in
connection with Rule 12g3-2(b): 82- N/A





Attached hereto and incorporated by reference herein is an unofficial English
translation of the Registrant's Immediate Report on an event or matter which
deviates from the Corporation's normal business, regarding the negotiations on
an investment in the Company in return for shares and warrants, which have been
filed with the Israeli Securities Authority.

This Form 6-K is hereby incorporated by reference into Tefron Ltd.'s
Registration Statement on Form F-3 (Registration No. 333-128847) and its
Registration Statements on Form S-8 (Registration Nos. 333-139021 and
333-111932).

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                                   SIGNATURES

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


                                          TEFRON LTD.
                                          (Registrant)

                                          By: /s/ Eran Rotem
                                          ----------------------
                                          Name: Eran Rotem
                                          Title: Chief Financial Officer


                                          By: /s/ Hanoch Zlotnik
                                          ----------------------
                                          Name: Hanoch Zlotnik
                                          Title: Treasurer

Date: September 27, 2010

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                                   TEFRON LTD.
                                 ("THE COMPANY")

       RE: IMMEDIATE REPORT ON AN EVENT OR MATTER WHICH DEVIATES FROM THE
     CORPORATION'S NORMAL BUSINESS, WHOSE SUBMISSION WAS DELAYED PURSUANT TO
                  REGULATION 36B OF THE SECURITIES REGULATIONS
                    ( PERIODIC AND IMMEDIATE REPORTS) - 1970

REGULATION 36 (B), (C) TO THE SECURITIES REGULATIONS (PERIODIC AND IMMEDIATE
REPORTS) - 1970

NATURE OF THE EVENT: NEGOTIATIONS ON AN INVESTMENT IN THE COMPANY IN RETURN FOR
SHARES AND WARRANTS

Tefron Ltd. (hereinafter: "THE COMPANY") hereby reports that on August 19, 2010
it signed a non-binding Memorandum of Understanding with a foreign company
operating in the Company's field of operations (hereinafter: "THE MEMORANDUM OF
UNDERSTANDING" and "THE INVESTOR", respectively), prior to executing a
transaction, which includes a cash investment in the Company amounting to
approximately four million US dollars and the transfer of certain assets from
the Investor to the Company, inter alia, a list of the Investor's customers, the
Investor's goodwill, the right to continue to engage with those customers of the
Investor and purchase orders (existing and future) from the Investor's
customers; in return for shares and warrants in the Company (hereinafter: "THE
TRANSACTION").

As mentioned, the Memorandum of Understanding which was signed between the
parties is not binding and at the present time the parties are negotiating for
the final and binding agreement. It should be emphasized, that there is no
certainty that the negotiations between the parties will result in a final
agreement and that the transaction will be completed. Signature on a final
agreement, should there be one, is subject to the completion of the negotiations
between the parties, completing a due diligence of the Company, agreement of the
Company's financing banks to the transaction and for the financing of part of
the transaction, and the approval of the Company's institutions.

It should be mentioned, that the Company's Board of Directors decided to approve
delaying the report of the negotiations with the Investor pursuant to the
provisions of Section 36(b) of the Securities Regulations (Periodic and
Immediate Reports) - 1970, after the Company's Board of Directors accepted the
Company's management's opinion, according to which the publication of this
Immediate Report might prevent a completion of the transaction or to
significantly worsen its terms. Nevertheless, due to the increases in the
share's price and trading volume on the Tel Aviv Stock Exchange Ltd. in recent
days, and in for caution's sake, it was decided to publish this Immediate Report
about the transactions, the Memorandum of Understanding signed, and the
negotiations between the Company and the Investor, because, in the Company's
opinion, it is possible that this information has reached the public due to
circumstances not dependent on the Company.

                                                    Yours sincerely,

                                                       ERAN ROTEM,
                                                 CHIEF FINANCIAL OFFICER
                                                     TEFRON LTD.

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