Convolutional neural networks (CNN) have been successfully applied to image super-resolution (SR) as well as other image restoration tasks. In this paper, we consider the problem of compressed video super-resolution. Traditional SR algorithms for compressed videos rely on information from the encoder such as frame type or quantizer step, whereas our algorithm only requires the compressed low resolution frames to reconstruct the high resolution video. We propose a CNN that is trained on both the spatial and the temporal dimensions of compressed videos to enhance their spatial resolution. Consecutive frames are motion compensated and used as input to a CNN that provides super-resolved video frames as output. Our network is pretrained with images, which significantly improves the performance over random initialization. In extensive experimental evaluations, we trained the state-of-the-art image and video superresolution algorithms on compressed videos and compared their performance to our proposed method.