Super-resolution (SR) algorithms for compressed video aim at recovering high-frequency information and estimating a high-resolution (HR) image or a set of HR images from a sequence of low-resolution (LR) video frames. In this paper we present a novel SR algorithm for compressed video based on the maximum a posteriori (MAP) framework. We utilize a new multichannel image prior model, along with the stateof-the art image prior and observation models. Moreover, relationship between model parameters and the decoded bitstream are established. Numerical experiments demonstrate the improved performance of the proposed method compared to existing algorithms for different compression ratios.