Exhibit 23.4

CONSENT OF INDEPENDENT ACCOUNTANTS

We hereby consent to the incorporation by reference in the Registration Statement on Form S-3 of Martin Midstream Partners L.P. of our report dated March 30, 2016 relating to the financial statements of West Texas LPG Pipeline Limited Partnership, which appears in the Annual Report on Form 10-K/A for the year ended December 31, 2015 of Martin Midstream Partners L.P. We also consent to the reference to us under the heading “Experts” in such Registration Statement.

/s/ PricewaterhouseCoopers LLP

Tulsa, Oklahoma

May 16, 2016