  In this paper, we investigate the mean curvature flow of submanifolds of
arbitrary codimension in $\mathbb{C}\mathbb{P}^m$. We prove that if the initial
submanifold satisfies a pinching condition, then the mean curvature flow
converges to a round point in finite time, or converges to a totally geodesic
submanifold as $t \rightarrow \infty$. Consequently, we obtain a new
differentiable sphere theorem for submanifolds in $\mathbb{C}\mathbb{P}^m$. Our
work improves the convergence theorem for mean curvature flow due to Pipoli and
Sinestrari {\cite{PiSi2015}}.
