Growing studies have shown that miRNAs are inextricably linked with many human diseases, and a great deal of effort has been spent on identifying their potential associations. Compared with traditional experimental methods, computational approaches have achieved promising results. In this article, we propose a graph representation learning method to predict miRNA-disease associations. Specifically, we first integrate the verified miRNA-disease associations with the similarity information of miRNA and disease to construct a miRNA-disease heterogeneous graph. Then, we apply a graph attention network to aggregate the neighbor information of nodes in each layer, and then feed the representation of the hidden layer into the structure-aware jumping knowledge network to obtain the global features of nodes. The output features of miRNAs and diseases are then concatenated and fed into a fully connected layer to score the potential associations. Through five-fold cross-validation, the average AUC, accuracy and precision values of our model are 93.30%, 85.18% and 88.90%, respectively. In addition, for three case studies of the esophageal tumor, lymphoma and prostate tumor, 46, 45 and 45 of the top 50 miRNAs predicted by our model were confirmed by relevant databases. Overall, our method could provide a reliable alternative for miRNA-disease association prediction.