Disease-gene association, an important problem in the biomedical area, can be used to early intervene the treat of deadly diseases. Recently, models based on graph convolutional networks (GCNs) have outperformed previous linear models on predicting the new disease-gene associations, due to its strong capability to capture the relevance of disease and gene in the new semantic embedding space. However, a single embedding vector cannot informatively represent a disease or gene and cannot characterize the uncertainty of their features. We propose to learn a distribution for a disease or gene under the variational autoencoder framework, which enables disease-gene associations to be modeled by the Kullback-Leibler divergence. The experiment results show that our model outperforms the state-of-the-art models significantly in various metrics.