•We analysed over 320 COVID-19 images and 320 healthy control images.•We proposed an improved CNN to extract individual image-level features.•We proposed to use GCN to extract relation-aware representations.•We proposed a DFF technology to combine features from GCN and CNN.•The proposed FCGNet gives better performance than 15 state-of-the-art approaches. (Aim) COVID-19 is an infectious disease spreading to the world this year. In this study, we plan to develop an artificial intelligence based tool to diagnose on chest CT images. (Method) On one hand, we extract features from a self-created convolutional neural network (CNN) to learn individual image-level representations. The proposed CNN employed several new techniques such as rank-based average pooling and multiple-way data augmentation. On the other hand, relation-aware representations were learnt from graph convolutional network (GCN). Deep feature fusion (DFF) was developed in this work to fuse individual image-level features and relation-aware features from both GCN and CNN, respectively. The best model was named as FGCNet. (Results) The experiment first chose the best model from eight proposed network models, and then compared it with 15 state-of-the-art approaches. (Conclusion) The proposed FGCNet model is effective and gives better performance than all 15 state-of-the-art methods. Thus, our proposed FGCNet model can assist radiologists to rapidly detect COVID-19 from chest CT images.