Recently, microRNAs (miRNAs) are confirmed to be important molecules within many crucial biological processes and therefore related to various complex human diseases. However, previous methods of predicting miRNA-disease associations have their own deficiencies. Under this circumstance, we developed a prediction method called deep representations-based miRNA-disease association (DRMDA) prediction. The original miRNA-disease association data were extracted from HDMM database. Meanwhile, stacked auto-encoder, greedy layer-wise unsupervised pre-training algorithm and support vector machine were implemented to predict potential associations. We compared DRMDA with five previous classical prediction models (HGIMDA, RLSMDA, HDMP, WBSMDA and RWRMDA) in global leave-one-out cross-validation (LOOCV), local LOOCV and fivefold cross-validation, respectively. The AUCs achieved by DRMDA were 0.9177, 08339 and 0.9156 +/- 0.0006 in the three tests above, respectively. In further case studies, we predicted the top 50 potential miRNAs for colon neoplasms, lymphoma and prostate neoplasms, and 88%, 90% and 86% of the predicted miRNA can be verified by experimental evidence, respectively. In conclusion, DRMDA is a promising prediction method which could identify potential and novel miRNA-disease associations.