Aiming at the face recognition problem, a new supervised dimensionality reduction algorithm is presented. On the basis of sparse representation theory, the proposed algorithm uses the within-class sparse construction to construct graph. This scheme can avoid the difficulty of parameter selection in traditional graph construction methods, and characterize the within-class information well. Furthermore, the multi-class nonparametric discriminant scatter is applied to characterize the between-class information, which will be more discriminative than parametric discriminant scatter in dealing with complex-distributed data. By maximizing the nonparametric between-class scatter and preserving the within-class sparse reconstructive relationship, the proposed algorithm can seek for the optimal projection matrix. Experimental results on ORL and Extended Yale B dataset show that the proposed method can achieve good recognition effect. 