microRNAs (miRNAs) are small non-coding RNAs related to a number of complicated biological processes. A growing body of studies have suggested that miRNAs are closely associated with many human diseases. It is meaningful to consider disease-related miRNAs as potential biomarkers, which could greatly contribute to understanding the mechanisms of complex diseases and benefit the prevention, detection, diagnosis and treatment of extraordinary diseases. In this study, we presented a novel model named Graph Convolutional Autoencoder for miRNA-Disease Association Prediction (GCAEMDA). In the proposed model, we utilized miRNA-miRNA similarities, disease-disease similarities and verified miRNA-disease associations to construct a heterogeneous network, which is applied to learn the embeddings of miRNAs and diseases. In addition, we separately constructed miRNA-based and disease-based sub-networks. Combining the embeddings of miRNAs and diseases, graph convolutional autoencoder (GCAE) was utilized to calculate association scores of miRNA-disease on two sub-networks, respectively. Furthermore, we obtained final prediction scores between miRNAs and diseases by adopting an average ensemble way to integrate the prediction scores from two types of subnetworks. To indicate the accuracy of GCAEMDA, we applied different cross validation methods to evaluate our model whose performances were better than the state-of-the-art models. Case studies on a common human diseases were also implemented to prove the effectiveness of GCAEMDA. The results demonstrated that GCAEMDA was beneficial to infer potential associations of miRNA-disease.