A spatio-temporal graph attention network for vehicle multimodal trajectory prediction (STGAMT) was proposed to address the challenges of predicting manually-driven vehicle trajectories and investigating their impact on autonomous driving decisions. The temporal and spatial characteristics were modeled based on the historical information about the vehicle. A two-dimensional convolutional neural network was employed to identify transverse and longitudinal lane change states, which were then combined with the output from the spatio-temporal dynamic interaction module to form transverse and longitudinal motion characteristics. The Softmax function was used to determine the vehicle’s driving intention. The multi-mode trajectory output was achieved by using a GRU network based on Gaussian conditional distribution. Experimental results showed that, in short-term predictions, the STGAMT model reduced the average error by 63.8% and 41.0% compared to the other five classic models on HighD and NGSIM datasets, respectively. In long-term predictions, the STGAMT model reduced the RMSE by 62.5% and 19.1% compared to the average RMSE of the other five classic models on HighD and NGSIM datasets, respectively. Results indicated that the STGAMT model could effectively improve the accuracy of manually-driven vehicle trajectory prediction.