To address the high uncertainty of pedestrian behavior and the complexity of the environment at traffic intersections, this paper proposes an innovative Spatio-temporal Variational Autoencoder model (ST-VAE). This model aims to efficiently capture the spatio-temporal characteristics of pedestrian behavior to enhance the accuracy of individual trajectory prediction at traffic intersections. To effectively handle the complex relationships in pedestrian social interactions, a Social Graph Attention Network (SGAT) was designed. This network dynamically identifies the relative importance among traffic participants and optimizes interaction analysis. Furthermore, a Complex Gated Recurrent Unit (CGRU) was introduced to accurately capture the dynamic changes in time series data, thereby optimizing future trajectory prediction. In the final prediction results, a Final Position Clustering (FPC) method was designed as a post-processing technique to eliminate bias and increase prediction accuracy. Evaluation results on four public datasets showed that the ST-VAE model reduces the average absolute error (ADE) and the final displacement error (FDE) by 27.2% and 18.2% respectively compared to the best baseline model,SocialCVAE, thereby demonstrating its significant performance advantage. Further ablation studies revealed the specific contributions of each component to the model’s performance, confirming the effectiveness and robustness of ST-VAE in handling diverse environments and complex interaction scenarios. The ST-VAE model not only provides a new perspective for pedestrian trajectory prediction technology but also offers solid technical support for the development of autonomous driving planning systems, showcasing the immense potential of deep learning in smart transportation system applications.