  In this paper, we mainly study the mean curvature flow in K\"ahler surfaces
with positive holomorphic sectional curvatures. First, we prove that if the
ratio $\lambda$ of the maximum and the minimum of the holomorphic sectional
curvatures $< 2$, then there exists a positive constant
$\delta>\frac{29(\lambda-1)}{\sqrt{(48-24\lambda)^{2}+(29\lambda-29)^{2}}}$
such that $\cos\alpha\geq\delta$ is preserved along the flow, improving the
main theorem in [LY]; Secondly, as similar as the main theorem in [HL0], we
prove that when $\cos\alpha$ is close to $1$ enough, then the symplectic mean
curvature flow exists for long time and converges to a holomorphic curve;
Finally, we prove that the symplectic mean curvature flow on K\"ahler surfaces
with $\lambda\leq 1+\frac{1}{200}$ exists for long time and converges to a
holomorphic curve if the initial surface satisfies a pinching condition, which
generalize one of the main theorems in [HLY].
