Traditional transient angle stability analysis methods do not fully consider the spatial characteristics of the network topology and the temporal characteristics of the time-series disturbance. Hence, a data-driven method is proposed in this study, combining graph convolution network and long short-term memory network (GCN-LSTM) to analyze the transient power angle stability by exploring the spatiotemporal disturbance characteristics of future power systems with high penetration of renewable energy sources (wind and solar energy) and power electronics. The key time-series electrical state quantities are considered as the initial input feature quantities and normalized using the Z-score, whereas the network adjacency matrix is constructed according to the system network topology. The normalized feature quantities and network adjacency matrix were used as the inputs of the GCN to obtain the spatial features, reflecting changes in the network topology. Subsequently, the spatial features are inputted into the LSTM network to obtain the temporal features, reflecting dynamic changes in the transient power angle of the generators. Finally, the spatiotemporal features are fused through a fully connected network to analyze the transient power angle stability of future power systems, and the softmax activation cross-entropy loss functions are used to predict the stability of the samples. The proposed transient power angle stability assessment method is tested on a 500 kV AC-DC practical power system, and the simulation results show that the proposed method could effectively mine the spatiotemporal disturbance characteristics of power systems. Moreover, the proposed model has higher accuracy, higher recall rate, and shorter training and testing times than traditional transient power angle stability algorithms.