This paper develops a novel graph convolutional network (GCN) framework for fault location in power distribution networks. The proposed approach integrates multiple measurements at different buses while taking system topology into account. The effectiveness of the GCN model is corroborated by the IEEE 123 bus benchmark system. Simulation results show that the GCN model significantly outperforms other widely-used machine learning schemes with very high fault location accuracy. In addition, the proposed approach is robust to measurement noise and data loss errors. Data visualization results of two competing neural networks are presented to explore the mechanism of GCNs superior performance. A data augmentation procedure is proposed to increase the robustness of the model under various levels of noise and data loss errors. Further experiments show that the model can adapt to topology changes of distribution networks and perform well with a limited number of measured buses.