  Given a cohomology $(1,1)$-class $\{\beta\}$ of compact Hermitian manifold
$(X,\omega)$ possessing a bounded potential and fixed a model potential $\phi$,
motivated by Darvas-Di Nezza-Lu and Li-Wang-Zhou's work, we show that
degenerate complex Monge-Amp\`ere equation $(\beta+dd^c \varphi)^n=e^{\lambda
\varphi}\mu$ has a unique solution in the relative full mass class
$\mathcal{E}(X,\beta,\phi)$, where $\mu$ is a non-pluripolar measure on $X$ and
$\lambda\geq0$ is a fixed constant.
  As an application, we give an explicit description of Lelong numbers of
elements in $\mathcal{E}(X,\beta,\phi)$ which generalized a theorem of
Darvas-Di Nezza-Lu in the Hermitian context.
