  Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where $\Delta $ is the
Laplacian operator on $\rz$, while the nonnegative potential $V$ belongs to
certain reverse H\"{o}lder class. In this paper, we establish some weighted
norm inequalities for commutators of Littlewood-Paley functions related to
Schr\"odinger operators.
