The deep neural network has achieved good results in medical image superresolution. However, due to the medical equipment limitations and the complexity of the human body structure, it is difficult to reconstruct clear cardiac magnetic resonance (CMR) superresolution images. To reconstruct clearer CMR images, we propose a CMR image superresolution (SR) algorithm based on multichannel residual attention networks (MCRN), which uses the idea of residual learning to alleviate the difficulty of training and fully explore the feature information of the image and uses the back-projection learning mechanism to learn the interdependence between high-resolution images and low-resolution images. Furthermore, the MCRN model introduces an attention mechanism to dynamically allocate each feature map with different attention resources to discover more high-frequency information and learn the dependency between each channel of the feature map. Extensive benchmark evaluation shows that compared with state-of-the-art image SR methods, our MCRN algorithm not only improves the objective index significantly but also provides richer texture information for the reconstructed CMR images, and our MCRN algorithm is better than the Bicubic algorithm in evaluating the information entropy and average gradient of the reconstructed image quality.