Research on algorithms and models to predict mean speeds in urban links plays an important role in the development of intelligent transportation information systems. The urban link mean speeds are affected by the stable factors like the topology of the regional traffic network, the recurrent factors like the time-varying traffic demands, and the incidental factors such as the bad weather, the traffic accidents, etc. To predict mean speeds of urban links in Xi’an, GCN-LSTM, a combined model of the Graph Convolutional Network (GCN) and the Long Short-Term Memory (LSTM) network was proposed. It is able to capture the stable factors and recurrent factors with spatial-temporal features to predict the urban link mean speeds in the regional traffic network. The LSTM is used to extract the temporal features of the mean speeds of the individual links, while the GCN is employed to extract the graphical topology features of the mean speeds of the individual links. The GCN-LSTM model can simultaneously combine the spatial-temporal correlation information. The experimental result shows that the proposed model can predict the urban link mean speeds more accurately than the other popular models. Therefore, the GCN-LSTM model can be supposed to contribute to making a decision for dynamic path plans in urban traffic network.