Biomedical evidence has demonstrated the relevance of microRNA (miRNA) dysregulation in complex human diseases, and determining the relationship between miRNAs and diseases can aid in the early detection and prevention of diseases. Traditional biological experimental methods have the disadvantages of high cost and low efficiency, which are well compensated by computational methods. However, many computational methods have the challenge of excessively focusing on the neighbor relationship, ignoring the structural information of the graph, and belittling the redundant information of the graph structure. This study proposed a computational model based on a graph-masking autoencoder named MGAEMDA. MGAEMDA is an asymmetric framework in which the encoder maps partially observed graphs into latent representations. The decoder reconstructs the masked structural information based on the edge and node levels and combines it with linear matrices to obtain the result. The empirical results on the two datasets reveal that the MGAEMDA model performs better than its counterparts. We also demonstrated the predictive performance of MGAEMDA using a case study of four diseases, and all the top 30 predicted miRNAs were validated in the database, providing further evidence of the excellent performance of the model.