The most important task in pedestrian trajectory prediction is to build a pedestrian trajectory interaction model. To address the lack of information about time and speed in the model, a spatio-temporal graph network algorithm with speed control is proposed to build a pedestrian interaction model and predict the trajectory. The overall model adopts a conditional adversarial network architecture, in which the velocity prediction module is used to predict the final velocity of the pedestrian as the control condition of the conditional adversarial network, and the velocity information is explicitly introduced into the pedestrian trajectory prediction to avoid the influence of large deviation of velocity on the trajectory. The spatio-temporal information fusion module based on the graphical convolutional attention mechanism is designed in the generator to explicitly encode the temporal correlation of pedestrian trajectory sequences while extracting their motion features and focusing on their spatial interactions. Finally, the trajectory prediction is completed by decoding the trajectory interaction features combining spatio-temporal and velocity information. In addition, considering the shortage of existing evaluation methods, the average number of collisions is used as the judgment of trajectory reasonableness. The experimental results show that the proposed algorithm can better predict the pedestrian trajectory with the average displacement error of 0.40m and the final displacement error of 0.79m.