Communication traffic prediction is of great guiding significance for communication planning management and improvement of communication service quality. However, due to the complex spatiotemporal correlation and uncertainty caused by the spatial topology and dynamic time characteristics of mobile communication networks, traffic prediction is facing enormous challenges. We propose a mobile traffic prediction method using dynamic spatiotemporal synchronous graph convolutional network (DSSGCN). DSSGCN has designed multiple components, which can effectively capture the heterogeneity in the local space-time map. More specifically, the network not only models the dynamic characteristics of nodes in the spatiotemporal graph of network traffic, but also captures the dynamic spatiotemporal characteristics of the edges of mobile service data with different time stamps. The outputs of these two components are fused by collaborative convolution to obtain the prediction results. Experiments on two ground truth mobile traffic datasets show that our DSSGCN model has good prediction performance.