Drug repositioning is an application-based solution based on mining existing drugs to find new targets, quickly discovering new drug-disease associations, and reducing the risk of drug discovery in traditional medicine and biology. Therefore, it is of great significance to design a computational model with high efficiency and accuracy. In this paper, we propose a novel computational method MGRL to predict drug-disease associations based on multi-graph representation learning. More specifically, MGRL first uses the graph convolution network to learn the graph representation of drugs and diseases from their self-attributes. Then, the graph embedding algorithm is used to represent the relationships between drugs and diseases. Finally, the two kinds of graph representation learning features were put into the random forest classifier for training. To the best of our knowledge, this is the first work to construct a multi-graph to extract the characteristics of drugs and diseases to predict drug-disease associations. The experiments show that the MGRL can achieve a higher AUC of 0.8506 based on five-fold cross-validation, which is significantly better than other existing methods. Case study results show the reliability of the proposed method, which is of great significance for practical applications.