Numerous experiments have shown that the occurrence of complex human diseases is often accompanied by abnormal expression of microRNA (miRNA). Identifying the associations between miRNAs and diseases is of great significance in the development of clinical medicine. However, traditional experimental methods are often time-consuming and inefficient. To this end, we proposed a deep learning method based on neighbor selection graph attention networks for predicting miRNA-disease associations (NSAMDA). Specifically, we firstly fused miRNA sequence similarity information and miRNA integrated similarity information to enrich miRNA feature information. Secondly, we used the fused miRNA feature information and disease integrated similarity information to construct a miRNA-disease heterogeneous graph. Thirdly, we introduced a neighbor selection method based on graph attention networks to select k-most important neighbors for aggregation. Finally, we used the inner product decoder to score miRNA-disease pairs. The results of five-fold cross-validation show that the mean AUC of NSAMDA is 93.69% on HMDD v2.0 dataset. In addition, case studies on the esophageal neoplasm, lung neoplasm and lymphoma were carried out to further confirm the effectiveness of the NSAMDA model. The results showed that the NSAMDA method achieves satisfactory performance on predicting miRNA-disease associations and is superior to the most advanced model.