When designing a vehicle, the most important variable that should be taken into account is the vehicle yaw rate, it represents an important indication of the vehicle’s stability and control. This paper aims to demonstrate how to simulate and control the yaw rate of a vehicle using two control methods, the first is the Linear Quadratic control method (LQR) and the other one is neural network control. The classical single-track model is prominently used for yaw stability control analysis. One driving conditions performed is the steering input; the steering input in this work is set as step steering angle and a lane change manoeuvre. Simulation results showed that both control methods used produced good and convergent performance results for the vehicle under different driving conditions.