Growing evidences have indicated that microRNAs (miRNAs) play a significant role relating to many important bioprocesses; their mutations and disorders will cause the occurrence of various complex diseases. The prediction of miRNAs associated with underlying diseases via computational approaches is beneficial to identify biomarkers and discover specific medicine, which can greatly reduce the cost of diagnosis, cure, prognosis, and prevention of human diseases. However, how to further achieve a more reliable prediction of potential miRNA-disease associations with effective integration of different biological data is a challenge for researchers. In this study, we proposed a computational model by using a federated method of combined multiple-similarities fusion and space projection (MSFSP). MSFSP firstly fused the integrated disease similarity (composed of disease semantic similarity, disease functional similarity, and disease Hamming similarity) with the integrated miRNA similarity (composed of miRNA functional similarity, miRNA sequence similarity, and miRNA Hamming similarity). Secondly, it constructed the weighted network of miRNA-disease associations from the experimentally verified Boolean network of miRNA-disease associations by using similarity networks. Finally, it calculated the prediction results by weighting miRNA space projection scores and the disease space projection scores. Leave-one-out cross-validation demonstrated that MSFSP has the distinguished predictive accuracy with area under the receiver operating characteristics curve (AUC) of 0.9613 better than that of five other existing models. In case studies, the predictive ability of MSFSP was further confirmed as 96 and 98% of the top 50 predictions for prostatic neoplasms and lung neoplasms were successfully validated by experimental evidences and supporting experimental evidences were also found for 100% of the top 50 predictions for isolated diseases.