We give a necessary and sufficient condition for positive Borel measures such that the Dirichlet problem, with zero boundary data, for the complex Monge-Ampere equation admits Holder continuous plurisubharmonic solutions. In particular, when the subsolution has finite Monge-Ampere total mass, we obtain an affirmative answer to a question of Zeriahi et al. (Complex Var. Elliptic Equ. 61(7): 902-930, 2016).