UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 6-K

REPORT OF FOREIGN ISSUER

PURSUANT TO RULE 13a-16 OR 15d-16

UNDER THE SECURITIES EXCHANGE ACT OF 1934

For the month of January, 2015

Commission file number: 1-10110

BANCO BILBAO VIZCAYA ARGENTARIA, S.A.

(Exact name of Registrant as specified in its charter)

BANK BILBAO VIZCAYA ARGENTARIA, S.A.

(Translation of Registrant’s name into English)

Paseo de la Castellana, 81

28046 Madrid

Spain

(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of 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):

Yes  ¨            No   x

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):

Yes  ¨            No   x

Banco Bilbao Vizcaya Argentaria, S.A. (BBVA), in compliance with the Securities Market legislation, hereby communicates the following:

RELEVANT EVENT

Following an update on its methodology, Moody’s Investor Service (Moody’s) has taken the following rating actions:

The rest of ratings and outlooks assigned to BBVA remain unchanged.

Madrid, January 21, 2015

SIGNATURE

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.