BACKGROUND: Predicting of chemical compounds is one of the fundamental tasks in bioinformatics and chemoinformatics, because it contributes to various applications in metabolic engineering and drug discovery. The recent rapid growth of the amount of available data has enabled applications of computational approaches such as statistical modeling and machine learning method. Both a set of chemical interactions and chemical compound structures are represented as graphs, and various graph-based approaches including graph convolutional neural networks have been successfully applied to chemical network prediction. However, there was no efficient method that can consider the two different types of graphs in an end-to-end manner. RESULTS: We give a new formulation of the chemical network prediction problem as a link prediction problem in a graph of graphs (GoG) which can represent the hierarchical structure consisting of compound graphs and an inter-compound graph. We propose a new graph convolutional neural network architecture called dual graph convolutional network that learns compound representations from both the compound graphs and the inter-compound network in an end-to-end manner. CONCLUSIONS: Experiments using four chemical networks with different sparsity levels and degree distributions shows that our dual graph convolution approach achieves high prediction performance in relatively dense networks, while the performance becomes inferior on extremely-sparse networks.