  In his recent work \cite{Y1}, X. Yang proved a conjecture raised by Yau in
1982 (\cite{Yau82}), which states that any compact K\"{a}hler manifold with
positive holomorphic sectional curvature must be projective. In this note, we
prove that any compact Hermitian manifold $X$ with positive real bisectional
curvature, its hodge number $h^{1,0}=h^{2,0}=h^{n-1,0}=h^{n,0}=0$. In
particular, if in addition $X$ is K\"{a}hler, then $X$ is projective. Also, it
is rationally connected manifold when $n=3$. This partially confirms the
conjecture 1.11 \cite{Y1} which is proposed by X. Yang.
