Because the existing Robust Principal Component Analysis (RPCA) approaches do not consider the continuity and the incompletion of sequential data, one type of low-rank matrix recovery model, named Regularized Incomplete RPCA (RIRPCA), was proposed. First, the model of RIRPCA was constructed based on a metric function for evaluating the continuity, where the model minimized a weighted combination of the matrix nuclear norm, L ₁ norm and regularized term. Then, the augmented Lagrange multipliers algorithm was employed to solve the proposed convex optimization problem. This algorithm has good scalability and low computation complexity. Finally, RIRPCA was applied to the background modeling of videos. The experimental results demonstrate that the proposed method has the superiority of recovering missing entries and separating foreground over matrix completion and incomplete RPCA.