Energy consumption prediction is crucial for planning and managing natural gas networks, enhancing transmission efficiency. However, most of relevant studies fail to consider the topology of natural gas network. Therefore, a multiscale graph based spatio-temporal graph convolutional network model (MG-STGCN) is proposed, which can extract the multi-scale relationship of data. Based on graph convolutional and temporal gated convolution network, data correlation, spatial dependence and time dependence are considered to improve the prediction effect. In order to verify the effect of the model, the model is tested based on two natural gas networks in different region of China. The single step prediction results of MG-STGCN are significantly better than spatio-temporal graph convolutional network (STGCN), long short-term memory (LSTM), gate recurrent unit (GRU) and temporal convolutional network (TCN), which proves the effectiveness and generalization ability of MG-STGCN. The training time of MG-STGCN is reduced by 20.8 % compared with STGCN. In different prediction time step, the average prediction effect of MG-STGCN is better than that of other methods, and the performance improvement rate is not less than 8.6 %. MG-STGCN can well capture the parameter correlation, spatial and temporal dependence of data, and achieve effective prediction of pipeline energy consumption.