FORM 6-K

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

Report of Foreign Private Issuer

Pursuant to rule 13a-16 or 15d-16 of

The Securities Exchange Act of 1934

For the month of December, 2015

National Bank of Greece S.A.

(Translation of registrant’s name into English)

86 Eolou Street, 10232 Athens, Greece

(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.]

[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.]

[If “Yes” is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-              ]

National Bank of Greece S.A.: Announcement on the coverage and payment of the Share Capital Increase and the payment of the Contingent Convertible Bonds of Greek law 3864/2010

Athens, December 9, 2015

Following the announcement of National Bank of Greece S.A. (the Bank) on December 4, 2015 by which the Bank informed investors on the results of the Public Offer in Greece of up to 1,000,000,000 new shares of nominal value and subscription price of €0.30 each (the Public Offer) which are issued in the context of a share capital increase to raise a total amount of up to €4,482 million, as decided by the Extraordinary General Meeting of the Bank’s shareholders held on November 17, 2015 (the Total SCI), the Bank announces, in accordance with applicable legislation, the following information relevant to the final coverage of the Total SCI and with respect to each part of it.

More specifically, the Bank’s Board of Directors in its meeting on December 8, 2015 determined the final amount by which the Total SCI was partially covered as well as the final total number of new, dematerialized, common, registered, voting shares of nominal value and subscription price €0.30 each (the New Shares). In particular, the Bank’s Board of Directors confirmed that the Total SCI was partially covered, in accordance with art. 13a of c.l. 2190/1920, i.e. it was covered by Euro 2,192,372,169,30 through the issuance of 7,307,907,231 New Shares. In the same meeting the Bank’s Board of Directors further certified that the aforementioned partial coverage is divided as follows:

A. increase by the amount of Euro 457,455,543.30 that was covered in cash by issuing 1,524,851,811 New Shares in the context of the International Offering;

B. increase by the amount of Euro 299,955,738.30 that was covered in cash by issuing 999,852,461  New Shares in the context of the Public Offer in Greece,

C. increase by the amount of Euro 694,906,185 that was covered in cash by the participants in the liability management exercise — Securities Exchange Offer and issuing thereby 2,316,353,950 New Shares,

D. increase by the amount of Euro 63,593,954.70 that was covered by contribution in kind that entailed the mandatory conversion to New Shares of liabilities of the Bank pursuant to the Cabinet Act no 45/7.12.2015 and the issuance thereunder in

favour of the relevant beneficiaries of the aforementioned liabilities (excluding the beneficiaries of the preference shares of the Bank existing at that time) of 211,979,849 New Shares;

E.  increase by the amount of Euro 676,460,748 that was covered by the Hellenic Financial Stability Fund (the HFSF) contributing to the Bank notes of the European Stability Mechanism (the ESM Notes) and issuing 2,254,869,160  New Shares, in accordance with art. 7 of Greek law 3864/2010 and Cabinet Act no 36/2.11.2015.

Pursuant to the aforementioned decision of the Bank’s Board of Directors, the latter approved the aforementioned allocation and disposal of 7,307,907,231 New Shares to new shareholders of the Bank.

It should also be noted that due to the issuance of Cabinet Act no 45/7.12.2015 all of the Bank’s preference shares were mandatorily converted (in accordance with the relevant provisions of article 6a of Greek law 3864/2010) to 1,603,700,987 common shares of the Bank.

Following the completion of the Total SCI and its partial coverage the Bank’s Board of Directors in its meeting on December 9, 2015 certified the partial payment as above of the Total SCI in cash and by contribution in kind, including the contribution of the ESM Notes, after their evaluation in accordance with article 7 par. 3 of Greek law 3864/2010, as currently applicable. Accordingly, the Bank’s Board of Directors confirmed, by also adjusting the relevant article in the Bank’s Articles of Association which described the Bank’s share capital, that the Bank’s share capital amounts today at Euro 2,744,145,458.10 divided into 9,147,151,527 common, registered, voting shares of nominal value €0.30 each.

The New Shares will be delivered to their beneficiaries in book entry form by crediting the relevant Investor Share and Securities Account in the Dematerialised Securities System, in accordance with information provided in the relevant subscriptions.

The date of crediting the New Shares and the date on which their trading on the Athens Exchange will commence will be notified to investors by a subsequent announcement of the Bank in accordance with applicable legislation.

Furthermore, the Bank’s Board of Directors in its meeting on December 8, 2015, decided, acting within the context of the relevant decision of the November 17, 2015 Extraordinary

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General Meeting of the Bank’s shareholders, the issuance of a convertible bond loan of a total amount of Euro 2,029,200,000 by issuing 20,292 contingent convertible bonds, of nominal value and subscription price of Euro 100,000 each, (the COCOs) which were all acquired by the HFSF, in accordance with par. 2 and 5c of Greek law 3864/2010, Cabinet Act no 36/2015 and Greek law 3156/2003, each as currently applicable. Following the execution of the relevant Subscription Agreement and the Bond Loan Programme concluded between the Bank and the HFSF, the Bank’s Board of Directors in its meeting on December 9, 2015 certified the contribution of ESM Notes valued at Euro 2,029,200,000 that fully covered the amount of the aforementioned bond loan, pursuant to the evaluation of such notes, in accordance with art. 7 par. 3 of Greek law 3864/2010, as applicable.

Following all the above, if the amount by which the Total SCI has been partially covered as above, in accordance with the relevant rules of c.l. 2190/1920, is added to the amounts by which the Group’s regulatory capital of Common Equity Tier 1 has been enforced, namely by means of: (a) the mandatory conversion of the Bank’s preference shares of article 4 indent xlvii of the Bank’s Articles of Association, (b) the capital gain deriving from the Securities Exchange Offer and (c) the issuance and full coverage of the COCOs by the HFSF, the resulting total amount is higher than the Bank’s capital shortfall under the Adverse Scenario, in accordance with the relevant decision of the Single Supervisory Mechanism (i.e. Euro 4,482 million).

For further information investors may contact the Bank’s Investor Relations Department (tel: 210- 2103343411, 412, 416, Mr John Nikolaou).

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This release is not an offer of securities for sale in the United States.  The securities to which this release relates have not been registered under the United States Securities Act of 1933, as amended (the “Securities Act”), and may not be offered or sold in the United States or to, or for the account or benefit of, U.S. persons, absent registration or an exemption from registration under the Securities Act.  There will be no public offering of the securities in the United States.

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This release contains certain forward-looking statements. These forward-looking statements involve risks and uncertainties that could significantly affect expected results and are based on certain key assumptions. Many factors could cause actual results to differ materially from those projected or implied in any forward-looking statements. Due to these uncertainties and risks, readers are cautioned not to place undue reliance on such forward-looking statements, which speak only as of the date of this announcement. National Bank of Greece S.A disclaims any obligation to update any forward-looking statements contained in this announcement, except as required pursuant to applicable law.

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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.

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