MicroRNAs (miRNAs) are short RNA molecular fragments that regulate gene expression by targeting and inhibiting the expression of specific RNAs. Due to the fact that microRNAs affect many diseases in microbial ecology, it is necessary to predict microRNAs' association with diseases at the microbial level. To this end, we propose a novel model, termed as GCNA-MDA, where dual-autoencoder and graph convolutional network (GCN) are integrated to predict miRNA-disease association. The proposed method leverages autoencoders to extract robust representations of miRNAs and diseases and meantime exploits GCN to capture the topological information of miRNA-disease networks. To alleviate the impact of insufficient information for the original data, the association similarity and feature similarity data are combined to calculate a more complete initial basic vector of nodes. The experimental results on the benchmark datasets demonstrate that compared with the existing representative methods, the proposed method has achieved the superior performance and its precision reaches up to 0.8982. These results demonstrate that the proposed method can serve as a tool for exploring miRNA-disease associations in microbial environments.