Accurate short-term solar and wind power predictions play an important role in the planning and operation of power systems. However, the short-term power prediction of renewable energy has always been considered a complex regression problem, owing to the fluctuation and intermittence of output powers and the law of dynamic change with time due to local weather conditions, i.e. spatio-temporal correlation. To capture the spatio-temporal features simultaneously, this paper proposes a new graph neural network-based short-term power forecasting approach, which combines the graph convolutional network (GCN) and long short-term memory (LSTM). Specifically, the GCN is employed to learn complex spatial correlations between adjacent renewable energies, and the LSTM is used to learn dynamic changes of power curves. The simulation results show that the proposed hybrid approach can model the spatio-temporal correlation of renewable energies, and its performance outperforms popular baselines on real-world datasets.