MicroRNAs (miRNAs) influence several biological processes involved in human disease. Biological experiments for verifying the association between miRNA and disease are always costly in terms of both money and time. Although numerous biological experiments have identified multi-types of associations between miRNAs and diseases, existing computational methods are unable to sufficiently mine the knowledge in these associations to predict unknown associations. In this study, we innovatively propose a heterogeneous graph attention network model based on meta-subgraphs (MSHGANMDA) to predict the potential miRNA-disease associations. Firstly, we define five types of meta-subgraph from the known miRNA-disease associations. Then, we use meta-subgraph attention and meta-subgraph semantic attention to extract features of miRNA-disease pairs within and between these five meta-subgraphs, respectively. Finally, we apply a fully-connected layer (FCL) to predict the scores of unknown miRNA-disease associations and cross-entropy loss to train our model end-to-end. To evaluate the effectiveness of MSHGANMDA, we apply five-fold cross-validation to calculate the mean values of evaluation metrics Accuracy, Precision, Recall, and F1-score as 0.8595, 0.8601, 0.8596, and 0.8595, respectively. Experiments show that our model, which primarily utilizes multi-types of miRNA-disease association data, gets the greatest ROC-AUC value of 0.934 when compared to other state-of-the-art approaches. Furthermore, through case studies, we further confirm the effectiveness of MSHGANMDA in predicting unknown diseases.