  In this short paper, for any holomorphic submersion $\pi: X\rightarrow B$, we
derive a criterion for $X$ to have K\"{a}hler structures. This criterion
generalizes Blanchard's criterion for a special class of isotrivial holomorphic
submersions. We use this criterion to answer a question of Harvey-Lawson in the
case of fiber dimension one. As the main application, we prove that the
existence of Hermitian-Symplectic structures on certain class of holomorphic
submersions with K\"{a}hler fibers and K\"{a}hler bases implies that the total
spaces are K\"{a}hler. This class includes isotrivial submersions and torus
fibrations.
