MicroRNAs (miRNAs) are a type of non-coding RNAs with about ∼22nt nucleotides. Increasing evidences have shown that miRNAs play critical roles in many human diseases. The identification of human disease-related miRNAs is helpful to explore the underlying pathogenesis of diseases. More and more experimental validated associations between miRNAs and diseases have been reported in the recent studies, which provide useful information for new miRNA-disease association discovery. In this study, we propose a computational framework, KBMF-MDI, to predict the associations between miRNAs and diseases based on their similarities. The sequence and function information of miRNAs are used to measure similarity among miRNAs while the semantic and function information of disease are used to measure similarity among diseases, respectively. In addition, the kernelized Bayesian matrix factorization method is employed to infer potential miRNA-disease associations by integrating these data sources. We applied this method to 6,084 known miRNA-disease associations and utilized 5-fold cross validation to evaluate the performance. The experimental results demonstrate that our method can effectively predict unknown miRNA-disease associations.