The most important task in pedestrian trajectory prediction is to establish a pedestrian trajectory interaction model. Aiming at the lack of semantic information about time and speed in the model, a spatial-temporal graph network algorithm combined with speed control is proposed to establish pedestrian interaction model and predict trajectory. The overall model adopts the conditional generative adversarial networks architecture, in which the speed prediction module is used to predict the future speed of pedestrians, and the control condition of the conditional generative adversarial networks. The speed information is explicitly introduced into the pedestrian trajectory prediction to avoid the influence of large deviation speed on the trajectory. A spatial-temporal information fusion module is designed in the generator. While extracting the motion features of pedestrian trajectory sequence and paying attention to its spatial interaction, it explicitly encodes the temporal correlation of pedestrian sequence. Finally, the trajectory interactive features combined with space-time information and speed information are decoded to complete the trajectory prediction. In addition, considering the shortcomings of the existing evaluation methods, the average collision times is used as the evaluation of trajectory rationality. The model is verified on the public datasets ETH and UCY. The experimental results show that the proposed algorithm can better complete the pedestrian trajectory prediction, with an average displacement error of 0. 40 m and a final displacement error of 0. 79 m.