Lots of research findings have indicated that miRNAs (microRNAs) are involved in many important biological processes; their mutations and disorders are closely related to diseases, therefore, determining the associations between human diseases and miRNAs is key to understand pathogenic mechanisms. Existing biological experimental methods for identifying miRNA–disease associations are usually expensive and time consuming. Therefore, the development of efficient and reliable computational methods for identifying disease-related miRNAs has become an important topic in the field of biological research in recent years. In this study, we developed a novel miRNA–disease association prediction model using a Laplacian score of the graphs and space projection federated method (LSGSP). This integrates experimentally validated miRNA–disease associations, disease semantic similarity scores, miRNA functional scores, and miRNA family information to build a new disease similarity network and miRNA similarity network, and then obtains the global similarities of these networks through calculating the Laplacian score of the graphs, based on which the miRNA–disease weighted network can be constructed through combination with the miRNA–disease Boolean network. Finally, the miRNA–disease score was obtained via projecting the miRNA space and disease space onto the miRNA–disease weighted network. Compared with several other state-of-the-art methods, using leave-one-out cross validation (LOOCV) to evaluate the accuracy of LSGSP with respect to a benchmark dataset, prediction dataset and compare dataset, LSGSP showed excellent predictive performance with high AUC values of 0.9221, 0.9745 and 0.9194, respectively. In addition, for prostate neoplasms and lung neoplasms, the consistencies between the top 50 predicted miRNAs (obtained from LSGSP) and the results (confirmed from the updated HMDD, miR2Disease, and dbDEMC databases) reached 96% and 100%, respectively. Similarly, for isolated diseases (diseases not associated with any miRNAs), the consistencies between the top 50 predicted miRNAs (obtained from LSGSP) and the results (confirmed from the above-mentioned three databases) reached 98% and 100%, respectively. These results further indicate that LSGSP can effectively predict potential associations between miRNAs and diseases.