Artifacts, blur and noise are the common distortions degrading MRI images during the acquisition process, and deep neural networks have been demonstrated to help in improving image quality. To well exploit global structural information and texture details, we propose a novel biomedical image enhancement network, named Feedback Graph Attention Convolutional Network (FB-GACN). As a key innovation, we consider the global structure of an image by building a graph network from image sub-regions that we consider to be node features, linking them non-locally according to their similarity. The proposed model consists of three main parts: 1) The parallel graph similarity branch and content branch, where the graph similarity branch aims at exploiting the similarity and symmetry across different image sub-regions in low-resolution feature space and provides additional priors for the content branch to enhance texture details. 2) A feedback mechanism with a recurrent structure to refine low-level representations with high-level information and generate powerful high-level texture details by handling the feedback connections. 3) A reconstruction to remove the artifacts and recover super-resolution images by using the estimated sub-region correlation priors obtained from the graph similarity branch. We evaluate our method on two image enhancement tasks: i) cross-protocol super resolution of diffusion MRI; ii) artifact removal of FLAIR MR images. Experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art methods.