Background and objective: Magnetic Resonance Image (MRI) analysis can provide anatomical examination of internal organs, which is helpful for diagnosis of the disease. Aiming at the problems of insufficient feature information mining in the process of MRI super-resolution (SR) reconstruction, the difficulty of determining the interdependence between the channels of the feature map, and the reconstruction error when reconstructing high-resolution (HR) images, we propose a SR method to solve these problems. Methods: In this work, we propose a gradual back-projection residual attention network for MRI super resolution (GRAN), which outperforms most of the state-of-the-art methods. Firstly, we use the gradual upsampling method to gradually scale the low-resolution (LR) image to a given magnification to alleviate the high-frequency information loss caused by the upsampling process. Secondly, we merge the idea of iterative back-projection at each stage of gradual upsampling, learn the mapping relationship between HR and LR feature maps and reduce the noise introduced during the upsampling process. Finally, we use the attention mechanism to dynamically allocate attention resources to the feature maps generated at different stages of the gradual back-projection network, so that the network model can learn the interdependence between each feature map. Results: For the 2 x and 4 x enlargement, the proposed GRAN method shows the superiority over the state-of-the-art methods on the Set5, Set14, and Urban100 benchmark datasets, extensive benchmark experiment and analysis show that the superiority of the GRAN algorithm in terms of peak signal-to-noise ratio and structural similarity index indicators. Conclusion: The MRI results reconstructed by gradual back-projection residual attention network on the public dataset IDI have good image sharpness, rich texture details and good visual experience. In addition, the reconstructed image is the closest to the real image, enabling the medical expert to see the biological tissue structure and its early pathological changes more clearly, providing assistance and support to the medical expert in the diagnosis and treatment of the disease. (c) 2021 Elsevier B.V. All rights reserved.