The development of new detection equipment and vehicle networking technology has enabled the acquisition of a significant quantity of accurate realtime vehicle trajectory data on urban roads, which is being utilized in the field of urban transportation research. However, due to the existence of diverse driving scenarios and random driving behavior on real roads, simple mathematical and theoretical models are insufficient to simulate complex real driving scenarios. Therefore, in this paper we present a data-driven model for predicting vehicle trajectories by means of Long Short-Term Memory (LSTM) cells with attention mechanism. The model is trained and tested using high-precision trajectory data coming from intersections of Beijing, China. The results illustrate that the improved Long Short-Term Memory model exhibits a lower prediction error in comparison to the previous model and other machine learning methods. It is capable of accurately reflecting the trajectory trend in terms of longitude prediction. The results of this research offer a theoretical basis for the enhancement of assisted driving systems and the creation of vehicle warning systems.