Autonomous driving technology can improve traffic safety and reduce traffic accidents. In addition, it improves traffic flow, reduces congestion, saves energy and increases travel efficiency. In the relatively mature automatic driving technology, the automatic driving function is divided into several modules: perception, decision-making, planning and control, and a reasonable division of labor can improve the stability of the system. Therefore, autonomous vehicles need to have the ability to predict the trajectory of surrounding vehicles in order to make reasonable decision planning and safety measures to improve driving safety. By using deep learning method, a safety-sensitive deep learning model based on short term memory (LSTM) network is proposed. This model can alleviate the shortcomings of current automatic driving trajectory planning, and the output trajectory not only ensures high accuracy but also improves safety. The cell state simulation algorithm simulates the trackability of the trajectory generated by this model. The research results show that compared with the traditional model-based method, the trajectory prediction method based on LSTM network has obvious advantages in predicting the trajectory in the long time domain. The intention recognition module considering interactive information has higher prediction and accuracy, and the algorithm results show that the trajectory is very smooth based on the premise of safe prediction and efficient lane change. And autonomous vehicles can efficiently and safely complete lane changes.