In this talk, we discuss a rigidity result for two dimensional graphical self-shrinker in $R^4$. That is a graph of $f(x):R^2\rightarrow R^2$ as a self-shrinker . Our idea is inspired from Mutao Wang’s results of graphical mean curvature flows with arbitrary codimension. If the Jacobian of $f$ is always less than $1$, then its graph as a self shrinker is a plane through 0.