Genomic profiles of cancer patients such as gene expression have become a major source to predict responses to drugs in the era of personalized medicine. As large-scale drug screening data with cancer cell lines are available, a number of computational methods have been developed for drug response prediction. However, few methods incorporate both gene expression data and the biological network, which can harbor essential information about the underlying process of the drug response. We proposed an analysis framework called DrugGCN for prediction of Drug response using a Graph Convolutional Network (GCN). DrugGCN first generates a gene graph by combining a Protein-Protein Interaction (PPI) network and gene expression data with feature selection of drug-related genes, and the GCN model detects the local features such as subnetworks of genes that contribute to the drug response by localized filtering. We demonstrated the effectiveness of DrugGCN using biological data showing its high prediction accuracy among the competing methods.