Increasing microRNAs (miRNAs) have been confirmed to be inextricably linked to various diseases, and the discovery of their associations has become a routine way of treating diseases. To overcome the time-consuming and laborious shortcoming of traditional experiments in verifying the associations of miRNAs and diseases (MDAs), a variety of computational methods have emerged. However, these methods still have many shortcomings in terms of predictive performance and accuracy. In this study, a model based on multiple graph convolutional networks and random forest (MGCNRF) was proposed for the prediction MDAs. Specifically, MGCNRF first mapped miRNA functional similarity and sequence similarity, disease semantic similarity and target similarity, and the known MDAs into four different two-layer heterogeneous networks. Second, MGCNRF applied four heterogeneous networks into four different layered attention graph convolutional networks (GCNs), respectively, to extract MDA embeddings. Finally, MGCNRF integrated the embeddings of every MDA into the features of the miRNA-disease pair and predicted potential MDAs through the random forest (RF). Fivefold cross-validation was applied to verify the prediction performance of MGCNRF, which outperforms the other seven state-of-the-art methods by area under curve. Furthermore, the accuracy and the case studies of different diseases further demonstrate the scientific rationale of MGCNRF. In conclusion, MGCNRF can serve as a scientific tool for predicting potential MDAs.