The rational use and dispatching of power energy are considered of paramount importance, and hence power load forecasting is one of the fundamental issues. The conventional power demand prediction method based on the statistical learning method may not perform well due to nonlinear and random factors of load, so researchers pay attention to the artificial intelligence in recent years, e.g. the artificial neural network (ANN) and machine learning (ML) and deep learning (DL). The deep learning tools have a good performance in power load forecasting, such as load forecasting based on time series. This paper presents a Graph Convolutional Network (GCN) based algorithmic solution for power demand forecasting. The proposed solution is extensively evaluated through the case study of real power distribution networks. The solution is evaluated based on the performance metrics including the mean square error of each prediction model Error (MSE) to measure the accuracy and robustness of the model. The numerical results confirmed that the proposed solution can well forecast the power demand rate in electricity stations.