Chest computed tomography (CT) scans of coronavirus 2019 (COVID-19) disease usually come from multiple datasets gathered from different medical centers, and these images are sampled using different acquisition protocols. While integrating multicenter datasets increases sample size, it suffers from inter-center heterogeneity. To address this issue, we propose an augmented multicenter graph convolutional network (AM-GCN) to diagnose COVID-19 with steps as follows. First, we use a 3-D convolutional neural network to extract features from the initial CT scans, where a ghost module and a multitask framework are integrated to improve the network's performance. Second, we exploit the extracted features to construct a multicenter graph, which considers the intercenter heterogeneity and the disease status of training samples. Third, we propose an augmentation mechanism to augment training samples which forms an augmented multicenter graph. Finally, the diagnosis results are obtained by inputting the augmented multi-center graph into GCN. Based on 2223 COVID-19 subjects and 2221 normal controls from seven medical centers, our method has achieved a mean accuracy of 97.76%. The code for our model is made publicly.(1)