Objective: To develop an end-to-end deep learning framework based on a protein-protein interaction (PPI) network to make synergistic anticancer drug combination predictions. Materials and Methods: We propose a deep learning framework named Graph Convolutional Network for Drug Synergy (GraphSynergy). GraphSynergy adapts a spatial-based Graph Convolutional Network component to encode the high-order topological relationships in the PPI network of protein modules targeted by a pair of drugs, as well as the protein modules associated with a specific cancer cell line. The pharmacological effects of drug combinations are explicitly evaluated by their therapy and toxicity scores. An attention component is also introduced in GraphSynergy, which aims to capture the pivotal proteins that play a part in both PPI network and biomolecular interactions between drug combinations and cancer cell lines. Results: GraphSynergy outperforms the classic and state-of-the-art models in predicting synergistic drug combinations on the 2 latest drug combination datasets. Specifically, GraphSynergy achieves accuracy values of 0.7553 (11.94% improvement compared to DeepSynergy, the latest published drug combination prediction algorithm) and 0.7557 (10.95% improvement compared to DeepSynergy) on DrugCombDB and Oncology-Screen datasets, respectively. Furthermore, the proteins allocated with high contribution weights during the training of GraphSynergy are proved to play a role in view of molecular functions and biological processes, such as transcription and transcription regulation. Conclusion: The introduction of topological relations between drug combination and cell line within the PPI network can significantly improve the capability of synergistic drug combination identification.