In this talk, we will present a discontinuous Galerkin (DG) finite element method for the nonlinear Schroding equation. The variational form is obtained after integrating by parts twice. $L^2$ Stability is proved by choosing the interfacial numerical fluxes carefully. The prior error estimated shows that this DG scheme gives the optimal orders of convergence in one dimensional space. Numerical examples shows that the scheme attains the optimal order of convergence for one and two dimensional spaces.