In this paper we proposed a robust video blocking artifacts reduction method based on low-rank theory and patch grouping. We separate video sequences into low-rank parts and sparse parts in order to improve the accuracy and robustness of the matrix completion problem. A Sigma filter is applied to the sparse parts for further denoising. Experimental results show the obvious effect of proposed method on reducing both blocking artifacts and isolation noise, meanwhile our method enhances the implementation efficiency by adopting Inexact Lagrange Multip-lier algorithm in matrix recovery and completion without any prediction in singular value decomposition or overlap on pixels afterwards.