We present a novel transient fault detection and classification approach in power transmission lines based on graph convolutional neural network. Compared with the existing techniques, the proposed approach considers explicit spatial information in sampling sequences as prior knowledge and it has stronger feature extraction ability. On this basis, a framework for transient fault detection and classification is created. Graph structure is generated to provide topology information to the task. Our approach takes the adjacency matrix of topology graph and the bus voltage signals during a sampling period after transient faults as inputs, and outputs the predicted classification results rapidly. Furthermore, the proposed approach is tested in various situations and its generalization ability is verified by experimental results. The results show that the proposed approach can detect and classify transient faults more effectively than the existing techniques, and it is practical for online transmission line protection for its rapidness, high robustness and generalization ability.