The interactions between the microbiota and the human host can affect the physiological functions of organs (such as the brain, liver, gut, etc.). Accumulating investigations indicate that the imbalance of microbial community is closely related to the occurrence and development of diseases. Thus, the identification of potential links between microbes and diseases can provide insight into the pathogenesis of diseases. In this study, we propose a deep learning framework (MDAGCAN) based on graph convolutional attention network to identify potential microbe-disease associations. In MDAGCAN, we first construct a heterogeneous network consisting of the known microbe-disease associations and multi-similarity fusion networks of microbes and diseases. Then, the node embeddings considering the neighbor information of the heterogeneous network are learned by applying graph convolutional layers and graph attention layers. Finally, a bilinear decoder using node embedding representations reconstructs the unknown microbe-disease association. Experiments show that our method achieves reliable performance with average AUCs of 0.9778 and 0.9454 ± 0.0038 in the frameworks of Leave-one-out cross validation (LOOCV) and 5-fold cross validation (5-fold CV), respectively. Furthermore, we apply MDAGCAN to predict latent microbes for two high-risk human diseases, i.e., liver cirrhosis and epilepsy, and results illustrate that 16 and 17 out of the top 20 predicted microbes are verified by published literatures, respectively. In conclusion, our method displays effective and reliable prediction performance and can be expected to predict unknown microbe-disease associations facilitating disease diagnosis and prevention.