Previous studies have confirmed microRNA (miRNA), small single-stranded non-coding RNA, participates in various biological processes and plays vital roles in many complex human diseases. Therefore, developing an efficient method to infer potential miRNA disease associations could greatly help understand operational mechanisms for diseases at the molecular level. However, during these early stages for miRNA disease prediction, traditional biological experiments are laborious and expensive. Therefore, this study proposes a novel method called AGAEMD (node-level Attention Graph Auto-Encoder to predict potential MiRNA Disease associations). We first create a heterogeneous matrix incorporating miRNA similarity, disease similarity, and known miRNA-disease associations. Then these matrixes are input into a node-level attention encoder-decoder network which utilizes low dimensional dense embeddings to represent nodes and calculate association scores. To verify the effectiveness of the proposed method, we conduct a series of experiments on two benchmark datasets (the Human MicroRNA Disease Database v2.0 and v3.2) and report the averages over 10 runs in comparison with several state-of-the-art methods. Experimental results have demonstrated the excellent performance of AGAEMD in comparison with other methods. Three important diseases (Colon Neoplasms, Lung Neoplasms, Lupus Vulgaris) were applied in case studies. The results comfirm the reliable predictive performance of AGAEMD.