Diabetic Retinopathy (DR) is a leading cause of blindness. It often happens to people who suffer from diabetes and seldom has early warning signs. Automatically DR detection and severity grading are helpful for clinicians by providing a second opinion. An automatic classification system classifies fundus images into 5 degrees of severity. In this paper, we propose a DR grading model based on lesion correlation graph using Graph Convolution Network (GCN) and Convolution Neural Network (CNN). We extract the irregular lesion region by calculating SURF descriptors in the fundus image. We then clusters descriptors into a number of cluster centroids which is regarded as node representation. With the assistance of GCN, we learn lesion correlation. After fusing correlation information and fundus image feature, which is derived from CNN model, we obtain the final classification result. Furthermore, we provide two evaluation measures: accuracy and Cohen's Kappa value for comparison on different experiments. So far, our model achieves good result in several DR datasets. Contribution- We introduce the idea of utilizing correlations among lesions learned by GCN to improve the grading result.