Accumulating evidence has shown that microbes play significant roles in human health and diseases. Therefore, identifying microbe-disease associations is conducive to disease prevention. In this article, a predictive method called TNRGCN is designed for microbe-disease associations based on Microbe-Drug-Disease Network and Relation Graph Convolutional Network (RGCN). First, considering that indirect links between microbes and diseases will be increased by introducing drug related associations, we construct a Microbe-Drug-Disease tripartite network through data processing from four databases including Human Microbe-Disease Association Database (HMDAD), Disbiome Database, Microbe-Drug Association Database (MDAD) and Comparative Toxicoge-nomics Database (CTD). Second, we construct similarity networks for microbes, diseases and drugs via microbe function similarity, disease semantic similarity and Gaussian interaction profile kernel similarity, respectively. Based on the similarity networks, Principal Component Analysis (PCA) is utilized to extract main features of nodes. These features will be input into the RGCN as initial features. Finally, based on the tripartite network and initial features, we design two-layer RGCN to predict microbe-disease associations. Experimental results indicate that TNRGCN achieves best performance in cross validation compared with other methods. Meanwhile, case studies for Type 2 diabetes (T2D), Bipolar disorder and Autism demonstrate the favorable effectiveness of TNRGCN in association prediction.