Abstract: In order to reduce the traffic accidents caused by lane departure, a control strategy of the lane keeping assistant based on linear quadratic regulator (LQR) was designed. On the basis of the lateral path offset and yaw error, the lateral velocity and yaw velocity were added as state variables. LQR algorithm was used to control the system to achieve stability, at the same time, the state of the vehicle was also fed back to the controller through CarSim, so as to minimize the cost function composed of state variables and control inputs. In other words, the steering wheel angle could be controlled at the minimum cost to realize the vehicle following the center line of the lane. The controller was built in MATLAB/Simulink and co-simulated with CarSim. The results show that under different vehicle speeds and road conditions, the control strategy can effectively reduce the control error, eliminate the lateral deviation and yaw deviation, ensure the stable driving of the vehicle in the lane at different speeds and road conditions, the controller has good robustness and adaptability.