In this paper, a novel joint sparse representation method is proposed for robust face recognition. We embed both group sparsity and kernelized locality-sensitive constraints into the framework of sparse representation. The group sparsity constraint is designed to utilize the grouped structure information in the training data. The local similarity between test and training data is measured in the kernel space instead of the Euclidian space. As a result, the embedded nonlinear information can be effectively captured, leading to a more discriminative representation. We show that, by integrating the kernelized local-sensitivity constraint and the group sparsity constraint, the embedded structure information can be better explored, and significant performance improvement can be achieved. On the one hand, experiments on the ORL, AR, extended Yale B, and LFW data sets verify the superiority of our method. On the other hand, experiments on two unconstrained data sets, the LFW and the IJB-A, show that the utilization of sparsity can improve recognition performance, especially on the data sets with large pose variation.