A three-dimensional (3D) deep learning method is proposed, which enables the rapid diagnosis of coronavirus disease 2019 (COVID-19) and thus significantly reduces the burden on radiologists and physicians. Inspired by the fact that the current chest computed tomography (CT) datasets are diversified in equipment types, we propose a COVID-19 graph in a graph convolutional network (GCN) to incorporate multiple datasets that differentiate the COVID-19 infected cases from normal controls. Specifically, we first apply a 3D convolutional neural network (3D-CNN) to extract image features from the initial 3D-CT images. In this part, a transfer learning method is proposed to improve the performance, which uses the task of predicting equipment type to initialize the parameters of the 3D-CNN structure. Second, we design a COVID-19 graph in GCN based on the extracted features. The graph divides all samples into several clusters, and samples with the same equipment type compose a cluster. Then we establish edge connections between samples in the same cluster. To compute accurate edge weights, we propose to combine the correlation distance of the extracted features and the score differences of subjects from the 3D-CNN structure. Lastly, by inputting the COVID-19 graph into GCN, we obtain the final diagnosis results. In experiments, the dataset contains 399 COVID-19 infected cases, and 400 normal controls from six equipment types. Experimental results show that the accuracy, sensitivity, and specificity of our method reach 98.5%, 99.9%, and 97%, respectively.