Let \pi:\mathbb{C}^n\times\mathbb{C}\rightarrow \mathbb{C} be the projection map onto the second factor and let D be a domain in \mathbb{C}^{n+1} such that for y\in\pi(D) , every fiber D_y:=D\cap\pi^{-1}(y) is a smoothly bounded strongly pseudoconvex domain in \mathbb{C}^n and is diffeomorphic to each other. By Chau's theorem, the Kähler-Ricci flow has a long time solution \omega_y(t) on each fiber X_y . This family of flows induces a smooth real (1,1)-form \omega(t) on the total space D whose restriction to the fiber D_y satisfies \omega(t)\vert_{D_y}=\omega_y(t) . In this paper, we prove that \omega(t) is positive for all t>0 in D if \omega(0) is positive. As a corollary, we also prove that the fiberwise Kähler-Einstein metric is positive semi-definite on D if D is pseudoconvex in \mathbb{C}^{n+1} .