  In this paper we prove a priori estimates for Donaldson's equation
$\omega\wedge(\chi+\sqrt{-1}\partial\bar{\partial}\varphi)^{n-1}=e^{F}(\chi+\sqrt{-1}\partial\bar{\partial}\varphi)^{n}$
over a compact Hermitian manifold X of complex dimension n, where $\omega$ and
$\chi$ are arbitrary Hermitian metrics. Our estimates answer a question of
Tosatti-Weinkove.
