It is known that miRNA plays an increasingly important role in many physiological processes. Disease-related miRNAs could be potential biomarkers for clinical diagnosis, prognosis, and treatment. Therefore, accurately inferring potential miRNAs related to diseases has become a hot topic in the bioinformatics community recently. In this study, we proposed a mathematical model based on matrix decomposition, named MFMDA, to identify potential miRNA-disease associations by integrating known miRNA and disease-related data, similarities between miRNAs and between diseases. We also compared MFMDA with some of the latest algorithms in several established miRNA disease databases. MFMDA reached an AUC of 0.9061 in the fivefold cross-validation. The experimental results show that MFMDA effectively infers novel miRNA-disease associations. In addition, we conducted case studies by applying MFMDA to three types of high-risk human cancers. While most predicted miRNAs are confirmed by external databases of experimental literature, we also identified a few novel disease-related miRNAs for further experimental validation.