For the purpose of solving the problems of missing edges and low segmentation accuracy in medical image segmentation, a medical image segmentation network (EAGC_UNet++) based on residual graph convolution UNet++ with edge attention gate (EAG) is proposed in the study. With UNet++ as the backbone network, the idea of graph theory is introduced into the model. First, the dropout residual graph convolution block (DropRes_GCN Block) and the traditional convolution structure in UNet++ are used as encoders. Second, EAGs are adopted so that the model pays more attention to image edge features during decoding. Finally, aiming at the imbalance problem of positive and negative samples in medical image segmentation, a new weighted loss function is introduced to enhance segmentation accuracy. In the experimental part, three datasets (LiTS2017, ISIC2018, COVID‐19 CT scans) were used to evaluate the performances of various models; multiple groups of ablation experiments were designed to verify the effectiveness of each part of the model. The experimental results showed that EAGC_UNet++ had better segmentation performance than the other models under three quantitative evaluation indicators and better solved the problem of missing edges in medical image segmentation.