Real-world video sequences coded at low bit rates suffer from compression artifacts, which are visually disruptive and can cause problems to computer vision algorithms. Unlike the denoising problem where the high frequency components of the signal are present in the noisy observation, most high frequency details are lost during compression and artificial discontinuities arise across the coding block boundaries. In addition to sparse spatial priors that can reduce the blocking artifacts for a single frame, temporal information is needed to recover the lost spatial details. However, establishing accurate temporal correspondences from the compressed videos is challenging because of the loss of high frequency details and the increase of false blocking artifacts. In this paper, we propose a non-causal temporal prior model to reduce video compression artifacts by propagating information from adjacent frames and iterating between image reconstruction and motion estimation. Experimental results on real-world sequences demonstrate that the deblocked videos by the proposed system have marginal statistics of high frequency components closer to those of the original ones, and are better input for standard edge and corner detectors than the coded ones.