Given a holomorphic mapping $f:{\mathbb{P}}^2\to {\mathbb{P}}^2$ of degree $d\ge 2$ we give sufficient conditions on a positive closed (1,1) current of $S$ of unit mass under which $d^{-n}{f}^{n*}S$ converges to the Green current as $n\to \infty$. We also conjecture necessary condition for the same convergence.