First NBC Bank Holding (FNBCQ) 10-Q 2016 Q2 Quarterly report

Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of First NBC Bank Holding Company (the “Company”) on Form 10-Q for the period ended June 30, 2016 (the “Report”), I, Ashton J. Ryan, Jr., President and Chief Executive Officer of the Company, certify 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 as of and for the periods covered in the Report.

/s/ Ashton J. Ryan, Jr.

Ashton J. Ryan, Jr.

President and Chief Executive Officer

October 20, 2016

A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request. The information furnished herein shall not be deemed to be filed for purposes of Section 18 of the Securities and Exchange Act of 1934, nor shall it be deemed incorporated by reference in any filing under the Securities Act of 1933.