Let $\Sigma$ be a compact oriented surface immersed in a four dimensional K\"ahler-Einstein manifold $(M, \omega)$. We consider the evolution of $\Sigma$ in the direction of its mean curvature vector. It is proved that being symplectic is preserved along the flow and the flow does not develop type I singularity. When $M$ has two parallel K\"ahler forms $\omega'$ and $\omega''$ that determine different orientations and $\Sigma$ is symplectic with respect to both $\omega'$ and $\omega''$, we prove the mean curvature flow of $\Sigma$ exists smoothly for all time. In the positive curvature case, the flow indeed converges at infinity.