Numerous experimental studies have indicated that alteration and dysregulation in mircroRNAs (miRNAs) are associated with serious diseases. Identifying disease-related miRNAs is therefore an essential and challenging task in bioinformatics research. Computational methods are an efficient and economical alternative to conventional biomedical studies and can reveal underlying miRNA-disease associations for subsequent experimental confirmation with reasonable confidence. Despite the success of existing computational approaches, most of them only rely on the known miRNA-disease associations to predict associations without adding other data to increase the prediction accuracy, and they are affected by issues of data sparsity. In this paper, we present MRRN, a model that combines matrix reconstruction with node reliability to predict probable miRNA-disease associations. In MRRN, the most reliable neighbors of miRNA and disease are used to update the original miRNA-disease association matrix, which significantly reduces data sparsity. Unknown miRNA-disease associations are reconstructed by aggregating the most reliable first-order neighbors to increase prediction accuracy by representing the local and global structure of the heterogeneous network. Five-fold cross-validation of MRRN produced an area under the curve (AUC) of 0.9355 and area under the precision-recall curve (AUPR) of 0.2646, values that were greater than those produced by comparable models. Two different types of case studies using three diseases were conducted to demonstrate the accuracy of MRRN, and all top 30 predicted miRNAs were verified.