Exhibit 32.1

Certification of United Continental Holdings, Inc.

Pursuant to 18 U.S.C. 1350

(Section 906 of the Sarbanes-Oxley Act of 2002)

Each undersigned officer certifies that to the best of his knowledge based on a review of the annual report on Form 10-K for the period ended December 31, 2014 of United Continental Holdings, Inc. (the “Report”):

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

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

Date: February 20, 2015

/s/ Jeffery A. Smisek

Jeffery A. Smisek

Chairman, President and

Chief Executive Officer

/s/ John D. Rainey

John D. Rainey

Executive Vice President and

Chief Financial Officer