Multiclass classification is an important problem in pattern recognition. Various classification methods have been proposed in the past few decades. However, most of these classification methods neglect the errors or the noises that exist in samples. As a result, classification accuracy is badly influenced by the errors or noises. In this paper, we propose a joint sparsity matrix learning method, which exploits -norm minimization to perform multiclass classification. In order to overcome the influence of the errors or noises, we introduce a sparse matrix to explicitly model the errors or noises and apply an iterative procedure to solve the -norm regularized problem. We perform experiments on four face databases to verify the effectiveness of the proposed method.