Background: Drug response prediction is an important problem in computational personalized medicine. Many machine learning-, especially deep learning-, based methods have been proposed for this task. However, these methods often represented the drugs as strings, which are not a natural way to depict molecules. Also, interpretation has not been considered thoroughly in these methods. Methods: In this study, we propose a novel method, GraphDRP, based on graph convolutional network for the problem. In GraphDRP, drugs are represented in molecular graphs directly capturing the bonds among atoms, meanwhile cell lines are depicted as binary vectors of genomic aberrations. Representative features of drugs and cell lines are learned by convolution layers, then combined to represent for each drug-cell line pair. Finally, the response value of each drug-cell line pair is predicted by a fully-connected neural network. Four variants of graph convolutional networks are used for learning the features of drugs. Results: We find that GraphDRP outperforms tCNN in all performance measures for all experiments. Also, through saliency maps of the resulting GraphDRP models, we discover the contribution of the genomic aberrations to the responses. Conclusion: Representing drugs as graphs are able to improve the performance of drug response prediction. Data and source code can be downloaded at https://github.com/hauldhut/GraphDRP.