COVID-19 pneumonia started in December 2019 and caused large casualties and huge economic losses. In this study, we intended to develop a computer-aided diagnosis system based on artificial intelligence to automatically identify the COVID-19 in chest computed tomography images. We utilized transfer learning to obtain the image-level representation (ILR) based on the backbone deep convolutional neural network. Then, a novel neighboring aware representation (NAR) was proposed to exploit the neighboring relationships between the ILR vectors. To obtain the neighboring information in the feature space of the ILRs, an ILR graph was generated based on the -nearest neighbors algorithm, in which the ILRs were linked with their -nearest neighboring ILRs. Afterward, the NARs were computed by the fusion of the ILRs and the graph. On the basis of this representation, a novel end-to-end COVID-19 classification architecture called neighboring aware graph neural network (NAGNN) was proposed. The private and public data sets were used for evaluation in the experiments. Results revealed that our NAGNN outperformed all the 10 state-of-the-art methods in terms of generalization ability. Therefore, the proposed NAGNN is effective in detecting COVID-19, which can be used in clinical diagnosis.