Emerging evidence shows that microRNAs (miRNAs) play a critical role in diverse fundamental and important biological processes associated with human diseases. Inferring potential disease related miRNAs and employing them as the biomarkers or drug targets could contribute to the prevention, diagnosis and treatment of complex human diseases. In view of that traditional biological experiments cost much time and resources, computational models would serve as complementary means to uncover potential miRNA–disease associations. In this study, we proposed a new computational model named Neighborhood Constraint Matrix Completion for MiRNA–Disease Association prediction (NCMCMDA) to predict potential miRNA–disease associations. The main task of NCMCMDA was to recover the missing miRNA–disease associations based on the known miRNA–disease associations and integrated disease (miRNA) similarity. In this model, we innovatively integrated neighborhood constraint with matrix completion, which provided a novel idea of utilizing similarity information to assist the prediction. After the recovery task was transformed into an optimization problem, we solved it with a fast iterative shrinkage-thresholding algorithm. As a result, the AUCs of NCMCMDA in global and local leave-one-out cross validation were 0.9086 and 0.8453, respectively. In 5-fold cross validation, NCMCMDA achieved an average AUC of 0.8942 and standard deviation of 0.0015, which demonstrated NCMCMDA’s superior performance than many previous computational methods. Furthermore, NCMCMDA was applied to three different types of case studies to further evaluate its prediction reliability and accuracy. As a result, 84% (colon neoplasms), 98% (esophageal neoplasms) and 98% (breast neoplasms) of the top 50 predicted miRNAs were verified by recent literature.