The automatic lane change assist system is an intelligent driving assistance technology oriented to traffic safety, which requires trajectory planning of the lane change maneuver based on the lane change decision. A typical scene of lane change for overtaking is selected, where the front vehicle in the same lane and the rear vehicle in the left lane are deemed to be potential dangerous vehicles through the lane change. Lane change trajectory equation is first established according to the general law of steering wheel angle through lane changes. Based on the relative position, velocity and acceleration information of the dangerous vehicles and the lane change vehicle, motions of these surrounding dangerous vehicles are predicted. At the same time, a multi-objective optimization function is established based on the relative longitudinal safety boundary. The objectives are the minimum safety distance, the lane change time and the front wheel angle. The trajectory planning algorithm of the lane change assist based on the model predictive control with multi-objective is then studied. The influences of prediction horizon, control horizon, road adhesion coefficient and vehicle speed on trajectory tracking are analyzed in this paper, and the robustness of the algorithm is then verified. In addition, the complexity of the model is simplified in considering of real-time demand while accuracy is still guaranteed. Simulation and experimental results show that the trajectory planning algorithm based on the model predictive control with multi - objective has greater improvements of those objectives of lane change compared with PID control. The proposed trajectory optimization algorithm can provide reference for the automatic lane change assist system.