An improved spatio-temporal graph convolutional networks traffic prediction algorithm, named free-flow reachable matrix-based spatio-temporal graph convolutional networks (FAST-GCN), was proposed, in order to predict real-time traffic flows accurately and improve the sensing and prediction of citywide traffic situation. The characteristics of urban complex road network structure were expressed effectively by the graph convolutional neural network, and the spatio-temporal dependency in complex road networks was explored by introducing free-flow reachable matrices. Thus the accuracy of traffic situation prediction was improved. First, preprocess traffic speeds and sensors location data. Second, with the existing spatio-temporal graph convolutional networks, the graph convolution module based on free flow reachable matrix was integrated to effectively capture the unique spatial characteristics of the urban traffic road networks. Finally, the prediction results were generated through a fully connected output layer. The proposed model was evaluated on a real-world traffic dataset PeMS. The experimental results show that this model could capture physical characteristics of road network and spatio-temporal dependency, and outperform the baselines such as spatio-temporal graph convolutional networks (STGCN), and the prediction accuracy in 45 minutes was improved by up to 5.656%. In addition, compared with baselines, the proposed model can adapt to traffic flow prediction in large-scale road networks and has superior scalability.