Many studies have clarified that microRNAs (miRNAs) are associated with many human diseases. Therefore, it is essential to predict potential miRNA-disease associations for disease pathogenesis and treatment. Numerous machine learning and deep learning approaches have been adopted to this problem. In this paper, we propose a Neural Inductive Matrix completion-based method with Graph Autoencoders (GAE) and Self-Attention mechanism for miRNA-disease associations prediction (NIMGSA). Some of the previous works based on matrix completion ignore the importance of label propagation procedure for inferring miRNA-disease associations, while others cannot integrate matrix completion and label propagation effectively. Varying from previous studies, NIMGSA unifies inductive matrix completion and label propagation via neural network architecture, through the collaborative training of two graph autoencoders. This neural inductive matrix completion-based method is also an implementation of self-attention mechanism for miRNA-disease associations prediction. This end-to-end framework can strengthen the robustness and preciseness of both matrix completion and label propagation. Cross validations indicate that NIMGSA outperforms current miRNA-disease prediction methods. Case studies demonstrate that NIMGSA is competent in detecting potential miRNA-disease associations.