Pedestrian trajectory prediction has broad applications in intelligent transportation, autonomous driving, and video surveillance. A key challenge in improving trajectory prediction accuracy lies in comprehensively modelling the complex interactions between pedestrians. Existing neural network-based modelling approaches face issues such as neglecting the sustained influence between pedestrians and the inability of static graph convolutional algorithms to adapt to dynamically changing graph structures. To address this issue, this paper proposes a trajectory prediction model based on a social-temporal graph, named STGCR (social-temporal graph cross-interaction transformer). The model quantifies the asynchronous interactions between pedestrians across different spatio-temporal contexts, integrates dynamic information between pedestrians, and applies it to graph convolution algorithms. Additionally, the STGCR introduces a spatio-temporal weighted attention mechanism to explicitly compute the relationships between pedestrians' spatial and temporal features. Experimental results show that, compared to the STAR model, the proposed model reduces the average displacement error and final displacement error by 39.6% and 30.8%, respectively, when predicting the next 8 time steps on publicly available datasets (ETH and UCY).