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Error concealment techniques are very important for video communication since compressed video sequences may be corrupted or lost when transmitted over error-prone networks. In this paper, we propose a novel two-stage error concealment scheme for erroneously received video sequences. In the first stage, we propose a novel spatio-temporal boundary matching algorithm (STBMA) to reconstruct the lost motion vectors (MV). A well defined cost function is introduced which exploits both spatial and temporal smoothness properties of video signals. By minimizing the cost function, the MV of each lost macroblock (MB) is recovered and the corresponding reference MB in the reference frame is obtained using this MV. In the second stage, instead of directly copying the reference MB as the final recovered pixel values, we use a novel partial differential equation (PDE) based algorithm to refine the reconstruction. We minimize, in a weighted manner, the difference between the gradient field of the reconstructed MB in current frame and that of the reference MB in the reference frame under given boundary condition. A weighting factor is used to control the regulation level according to the local blockiness degree. With this algorithm, the annoying blocking artifacts are effectively reduced while the structures of the reference MB are well preserved. Compared with the error concealment feature implemented in the H.264 reference software, our algorithm is able to achieve significantly higher PSNR as well as better visual quality.