I will discuss the regularity of bounded ω-plurisubharmonic solutions of the complex Monge-Ampère equation (ω + dd^c φ)^n= e^{−F(φ,z)} ω^n on a compact Hermitian manifold. Székelyhidi and Tosatti proved that on a compact Kähler manifold such weak solutions are smooth. Their result can be extended to Hermitian case with an extra assumption.