Separation of video clips into foreground and background components is a useful and important technique, making recognition, classification, and scene analysis more efficient. In this paper, we propose a motion-assisted matrix restoration (MAMR) model for foreground-background separation in video clips. In the proposed MAMR model, the backgrounds across frames are modeled by a low-rank matrix, while the foreground objects are modeled by a sparse matrix. To facilitate efficient foreground-background separation, a dense motion field is estimated for each frame, and mapped into a weighting matrix which indicates the likelihood that each pixel belongs to the background. Anchor frames are selected in the dense motion estimation to overcome the difficulty of detecting slowly moving objects and camouflages. In addition, we extend our model to a robust MAMR model against noise for practical applications. Evaluations on challenging datasets demonstrate that our method outperforms many other state-of-the-art methods, and is versatile for a wide range of surveillance videos.