Increasing evidence has indicated that microRNAs (miRNAs) are associated with numerous human diseases. Studying the associations between miRNAs and diseases contributes to the exploration of effective diagnostic and treatment approaches for diseases. Unfortunately, the use of biological experiments to reveal the potential associations between miRNAs and diseases is time consuming and costly. Therefore, it is very necessary to use simple and efficient calculation models to predict potential disease-related miRNAs. Considering the limitations of other previous methods, we proposed a novel computational model of Symmetric Nonnegative Matrix Factorization for MiRNA-Disease Association prediction (SNMFMDA) to reveal the relation of miRNA-disease pairs. SNMFMDA could be applied to predict miRNAs associated with new diseases. Compared to the direct use of the integrated similarity in previous computational models, the integrated similarity need to be interpolated by symmetric non-negative matrix factorization (SymNMF) before application in SNMFMDA, and the relevant probability of disease-miRNA was obtained mainly through Kronecker regularized least square (KronRLS) method in our model. What's more, the AUC of global leave-one-out cross validation (LOOCV) reached 0.9007, and the AUC based on local LOOCV was 0.8426. Besides, the mean and the standard deviation of AUCs achieved 0.8830 and 0.0017 respectively in 5-fold cross validation. All of the above results demonstrated the superior prediction performance of SNMFMDA. We also conducted three different case studies on Esophageal Neoplasms, Breast Neoplasms and Lung Neoplasms, and 49, 49, and 48 of the top 50 of their predicted miRNAs respectively were confirmed by databases or related literatures. It could be expected that SNMFMDA would be a model with the ability to predict disease-related miRNAs efficiently and accurately.