Aiming at the yaw problem of the flat tire vehicle, the model predictive control (MPC) based front wheel steering controller is proposed to correct the vehicle yaw and ensure the vehicle to run on the safe path. Based on the model predictive control, the simplified double track vehicle model is selected, and the vehicle motion state is described by differential equation. The prediction equation is derived by linear discretization. Considering the vehicle stability factor, it is added as a constraint condition and transformed into the standard quadratic form to calculate the optimal solution. The closed-loop system is constructed for simulation. The results show that the MPC based design has good performance: The front wheel active steering controller can keep the vehicle running stably under two driving conditions of straight driving and double shifting driving, and effectively control the running track of the flat tire vehicle. The center of mass side slip angle, tire side slip angle and yaw angle speed are all within the stability requirements, so as to ensure the vehicle to drive in the safe path and achieve the trajectory control effect of the tire burst vehicle.