Increasing evidence has suggested that microRNAs (miRNAs) may function as positive regulators at the post-transcriptional level. A search for associations between miRNAs and diseases is crucial for understanding the pathogenesis. Various publicly available databases have been constructed to store meaningful information on a large number of miRNA molecules. In this study, to resolve the limitation that individual sources of miRNA target data tend to be incomplete and noisy, we propose a network-based computational method called self-weighting for integrating multiple data sources. A bipartite phenotype-miRNA network (BPMN) incorporates known disease-miRNA interactions as well as the similarities between disease phenotypes and functional similarities of miRNAs. Random walk with restart algorithm was deployed on the bipartite network to predict novel disease-miRNA associations. In leave-one-out cross-validation experiments, our technique achieves an AUC of 0.801 when evaluating against known disease-related miRNAs from HMDD. Systematic prioritization of miRNAs for 11 common diseases obtained an average AUC of 0.765. Additionally, a case study on colon cancer uncovered a number of potential miRNA candidates as biomarkers of this disease.