Accurate and efficient short-term traffic flow prediction is one of the basic guarantees for solving various traffic problems. According to the road network topology and the temporal and spatial correlation of traffic flow, a multi-step road network speed prediction method based on graph convolution-long short-term memory neural network (GCLSTM) is proposed. Firstly, the weight parameters of the convolutional layer are designed to increase the connection between the convolutional layers. Convolutional layer is embedded in the gating unit of long short-term memory neural network (LSTM) to achieve the effect of capturing the spatial and temporal correlation at the same time. Secondly, an encoder and decoder structure is used to realize multi-step prediction. The structure gradually increase the output sequence length to improve the efficiency of model training. Finally, ablation experiments and comparison experiments are performed on the expressway dataset and the urban road dataset. The ablation experiments show that the error index of the hybrid network prediction model is significantly reduced. The comparative experiments exhibit that the GCLSTM prediction model has higher multi-step prediction accuracy and better prediction performance at a single observation point. This model provides accurate prediction information for intelligent transportation.