Under the case of low adhesion road，an improved control algorithm is proposed to solve the problem of the lack of accuracy and stability in the path tracking of autonomous vehicles based on Linear Time-Varying Model Predictive Control （LTVMPC）. Based on vehicle dynamics，the slip angles and ratios of four tires are accurately expressed as the nonlinear function of vehicle state parameters. The Jacobian matrix is obtained by taking wheel speed as constant when linearizing the vehicle state equation in prediction horizon so as to reduce the dimension of the system，which aims to establish the improved 3-DOF vehicle model. The yaw rate tracking error is added into the performance index of quadratic programming to improve the path tracking performance and the influence of the slip angle of vehicle on the tracking accuracy and vehicle stability is considered to modify the reference yaw angle，which improves the overall performance of LTVMPC. The double lane change tracking simulation under the condition of low adhesion coefficient is performed on Carsim-Simulink co-simulation platform，and the results show that the improved control algorithm can increase the accuracy of path tracking and stability of vehicle while ensuring real-time performance.