She also quit the same post at the Thailand Convention and Exhibition Bureau (TCEB). Her letters said the resignations took effect on Friday.
Rear Adm Noppadon Ruangsamai of the National Council for Peace and Order (NCPO) said the NCPO would decide what to do to find her successors.
Ms Pensuda is the latest of several state enterprise chairmen to resign to pave the way for the NCPO to purge the boards of political influence and cut back what have been perceived as excessive benefits.
Suwat Sidthilaw, permanent secretary of the Tourism and Sports Ministry, said the process of recruiting the new TAT governor to replace Thawatchai Arunyik, whose term will end in March 2015, was still under way and applications would be accepted until July 4.