In 2019, coronavirus disease (COVID-19) is an acute disease that can rapidly develop into a very serious state. Therefore, it is of great significance to realize automatic COVID-19 diagnosis. However, due to the small difference in the characteristics of computed tomography (CT) between community acquire pneumonia (CP) and COVID-19, the existing model is unsuitable for the three-class classifications of healthy control, CP and COVID-19. The current model rarely optimizes the data from multiple centers. Therefore, we propose a diagnosis model for COVID-19 patients based on graph enhanced 3D convolution neural network (CNN) and cross-center domain feature adaptation. Specifically, we first design a 3D CNN with graph convolution module to enhance the global feature extraction capability of the CNN. Meanwhile, we use the domain adaptive feature alignment method to optimize the feature distance between different centers, which can effectively realize multi-center COVID-19 diagnosis. Our experimental results achieve quite promising COVID-19 diagnosis results, which show that the accuracy in the mixed dataset is 98.05%, and the accuracy in cross-center tasks are 85.29% and 87.53%.