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 April, 2016

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)

Calle Azul, 4

28050 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 securities market legislation, hereby proceeds by means of the present document to notify the following:

RELEVANT EVENT

BBVA has agreed to carry out an issue of perpetual contingent convertible securities, convertible into newly issued ordinary shares of BBVA (the “Preferred Securities”), without pre-emption rights, for a total amount of 1 billion Euros (the “Issuance”). BBVA has applied for the Preferred Securities to qualify as Additional Tier 1 Capital under Law 10/2014, of 26th June, on regulation, supervision and solvency of credit entities and Regulation (EU) No. 575/2013 of the European Parliament and of the Council of 26 June 2013, on prudential requirements for credit institutions and investment firms.

The Issuance is targeted only at qualified investors and foreign private banking customers and in any case will not be made to, and may not be subscribed for, in Spain or by Spanish residents, without prejudice to the additional sales restrictions as set out in the terms and conditions of the Issuance.

Madrid, April 7^th, 2016

Important information:

This announcement is not an offer of securities for sale in the United States or any other jurisdiction. The Preferred Securities may not be offered or sold in the United States absent registration under the U.S. Securities Act of 1933, as amended, or an exemption therefrom. BBVA has not and does not intend to register the Preferred Securities under the U.S. Securities Act of 1933, as amended, and is not offering or selling the Preferred Securities in the United States. No money, securities or other consideration from any person inside the United States is being solicited and, if sent in response to the information contained in this announcement, will not be accepted. Further restrictions apply in, among other jurisdictions, the United Kingdom, Spain, Singapore, Hong Kong, Canada and Switzerland, as set out in the offering documentation.

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.