Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in this Registration Statement on Form S-8 of KemPharm, Inc. of our report dated March 1, 2019, relating to the financial statements of KemPharm, Inc., appearing in the Annual Report on Form 10-K of KemPharm, Inc. for the year ended December 31, 2018.

/s/ RSM US LLP

Orlando, Florida

March 1, 2019