A graph attention stacking autoencoder approach for predicting the association between microorganisms and drugs, known as GATSAE, is proposed in response to the conventional method of finding new associations between microorganisms and drugs, which is primarily accomplished through biological experiments, which is highly costly and time-consuming. Firstly, establish a heterogeneous network of microorganisms and drugs to enrich the associated information. Secondly, the convolutional fusion matrix of microorganisms and drugs is obtained by extracting multi-layer latent features through graph convolutional network (GCN). Once again, an improved stacked autoencoder is used to learn unsupervised low dimensional representations of meaningful high-order similar features. Graph convolution and attention mechanisms are added to the stacked autoencoder to further optimize the extraction of high-order feature information. Finally, the low-dimensional features are concatenated with associated features, and a multi-layer perceptron (MLP) is used to score and predict the final microbial drug. According to performance evaluation, GATSAE subjects’ area under the receiver operating characteristic curve (AUROC) and area under the precision-recall curve (AUPR) were 0.9619 and 0.9577, respectively. These results are better than those of popular deep learning techniques and traditional machine learning techniques. Case studies have shown that GATSAE can accurately predict candidate drugs related to SARS-CoV-2 and Escherichia coli, as well as candidate microorganisms related to aspirin.