In the recent few years, plenty of research has shown that microRNA (miRNA) is likely to be involved in the formation of many human diseases. So effectively predicting potential associations between miRNAs and diseases helps to understand the development and treatment of diseases. In this study, an edge perturbation based method is proposed for predicting potential miRNA-disease association (EPMDA). Different from the previous studies, we design an feature vector to describe each edge of a graph by structural Hamiltonian information. Moreover, the extracted features are used to train a multi-layer perception model to predict the candidate disease-miRNA associations. The experimental results on the HMDD dataset show that EPMDA achieves the AUC value of 0.9818 through 5-fold cross-validation, which improves the AUC values by approximately 3.5 percent compared to the latest method DeepMDA. For the leave-one-disease-out cross-validation, EPMDA achieves the AUC value of 0.9371, which improves the AUC values by approximately 7.4 percent compared to DeepMDA. In the case study, we verify the prediction performance of EPMDA on three human diseases. As a result, there are 42, 46, and 41 of the top 50 predicted miRNAs for these three diseases which are confirmed by the published experimental discoveries, respectively.