Face recognition is active in the field of computer vision and pattern recognition and has extremely wide-spread application prospect. However, the problem that both training images and testing images are corrupted is not well solved in face recognition task. To address such a problem, this paper proposes a novel Discriminative Low-Rank Dictionary Learning for Low-Rank Sparse Representation algorithm (DLRD_LRSR) aiming to learn a pure dictionary. We suggest each sub dictionary and sparse representation be low-rank for reducing the effect of noise in training samples and introduce a novel discriminative reconstruction error term to make the coefficient more discriminating. We demonstrate the effectiveness of our approach on three public face datasets. Our method is more effective and robust than the previous competitive dictionary learning method.