In this thesis, we introduce an adaptive finite element method for solving the KohnSham equation. With this new method, solving the Kohn-Sham equation is transformed to solve a series of boundary value problems on multilevel finite element spaces and a series of nonlinear eigenvalue problems on the coarsest finite element spaces. Based on this method, a priori estimate for the eigenpair approximation and the residual method a posteriori error estimation for the Kohn-Sham model are used to refine the mesh and improve the accuracy. In all, the proposed adaptive finite element method can improve the overall efficiency for solving nonlinear eigenvalue problem .