Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of First NBC Bank Holding Company (the “Company”) on Form 10-K for the fiscal year ended December 31, 2013 (the “Report”), I, Ashton J. Ryan, Jr., President and Chief Executive Officer of the Company, certify, to the best of my knowledge, pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Ashton J. Ryan, Jr.

Ashton J. Ryan

President and Chief Executive Officer

March 31, 2014