Sparse representation model (SRM) has been widely used in many image processing and computer vision tasks. However, the conventional SRM usually neglects the prior knowledge about similar signals. Considering the fact that similar signals also have subtle differences, in this paper we propose a robust bi-sparsity model (RBSM) to effectively exploit the prior knowledge about the similarities and the distinctions of signals. In RBSM, similar signals are encouraged to be coded on the same sub-dictionary. But the distinctiveness of similar signals is also addressed by imposing the l-norm regularization on the difference between each coefficient and its non-local means. In addition, a weight vector is incorporated into the loss function to make the proposed model robust to outliers. We apply RBSM for mixed noise reduction and experimental results show that our proposed model is superior to several state-of-the-art mixed noise removal methods.