Aiming at the problems of insufficient fraud samples, expensive data labeling and low accuracy of traditional Euclidean space model, a new One-Class medical insurance fraud detection model based on Graph convolution and Variational Auto-Encoder (OCGVAE) was proposed. Firstly, a social network was established through patient visit records, the weight relationships between the patients and the doctors were calculated, and a 2-layer Graph Convolutional neural Network (GCN) was designed as the input of the social network data to reduce the data dimension of the social network. Secondly, a Variational Auto-Encoder (VAE) was designed to implement the model training under only one-class fraud sample label. Finally, a Logistic Regression (LR) model was designed to discriminate the data category. The experimental results show that the detection accuracy of the OCGVAE model reaches 87.26%, which is 16.1%,70.2%,31.7%,36.5%,and 27.6% higher than that of One-Class Adversarial Net (OCAN), One-Class Gaussian Process (OCGP), One-Class Nearest Neighbor (OCNN), One-Class Support Vector Machine (OCSVM) and Semi-supervised GCN (Semi-GCN) algorithm, demonstrating that the proposed model effectively improves the accuracy of medical insurance fraud screening.