Vehicle trajectory prediction is a crucial component of autonomous driving systems, and improving its reliability and accuracy greatly enhances the safety of autonomous driving. Considering the influence of traffic conditions on vehicle movement, this study focuses on traffic environmental factors such as neighboring vehicle motion and relative spatial positions. Building on the Long Short-Term Memory (LSTM) network encoder-decoder model, a spatiotemporal attention mechanism is introduced. Temporal-level attention focuses on the historical trajectories of the target and neighboring vehicles, whereas spatial attention focuses on the relative spatial positions of the vehicles. Additionally, to enhance feature extraction and achieve a more comprehensive feature fusion, multi-scale convolutional social pooling is utilized to increase the receptive field and integrate multi-scale features. By combining these two aspects, this study proposes a vehicle trajectory prediction model called MCS-STA-LSTM, which incorporates the LSTM encoder-decoder architecture, multi-scale convolutional social pooling, and a spatiotemporal attention mechanism. This model learns the interdependencies of vehicle movements to obtain multi-modal prediction distributions of future trajectories for a target vehicle based on maneuver categories. The model is trained, validated, and tested on the publicly available NGSIM dataset. Several comparative experiments demonstrate that the MCS-STA-LSTM model achieves an average Root Mean Square Error (RMSE) reduction of 9.35% within 3 s and 5.53% within 5 s when compared to other trajectory prediction models. These results indicate an improved trajectory prediction accuracy, highlighting the model's advantage in medium- and short-term predictions.