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In this paper, we mainly study the mean curvature flow in K\"ahler surfaceswith positive holomorphic sectional curvatures. First, we prove that if theratio $\lambda$ of the maximum and the minimum of the holomorphic sectionalcurvatures $< 2$, 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 themain theorem in [LY]; Secondly, as similar as the main theorem in [HL0], weprove that when $\cos\alpha$ is close to $1$ enough, then the symplectic meancurvature flow exists for long time and converges to a holomorphic curve;Finally, we prove that the symplectic mean curvature flow on K\"ahler surfaceswith $\lambda\leq 1+\frac{1}{200}$ exists for long time and converges to aholomorphic curve if the initial surface satisfies a pinching condition, whichgeneralize one of the main theorems in [HLY].

Remarks on symplectic mean curvature flows in K\"ahler surfaces with positive holomorphic sectional curvatures