In this paper, we generalize Medos-Wang's arguments and results on the mean
curvature flow deformations of symplectomorphisms of $\CP^n$ in \cite{MeWa} to
complex Grassmann manifold $G(n, n+m;\C)$ and compact totally geodesic
K\"ahler-Einstein submanifolds of $G(n, 2n;\C)$ such as irreducible Hermitian
symmetric spaces $SO(2n)/U(n)$ and $Sp(n)/U(n)$ (in the terminology of \cite[p.
518]{He}). Our pinched condition is weaker, even if for $\CP^n$. We also give
an abstract result and discuss the case of complex tori.