A direct yaw moment controller algorithm was designed based on a model reference adaptive control (MRAC) to improve the lateral stability and safety for four-wheel independent electric vehicles (EV). The upper-level controller was based on the Lyapunov function to estimate the tire corning stiffness and vehicle mass in real-time and obtain the additional yaw moment. The lower-level controller allocated the requested yaw moment to each wheel via an optimized quadratic programming algorithm, and guarantees the real-time dynamic response of the controller. The results from Carsim and Simulink co-simulation under double lane change driving mode show that the proposed MRAC controller algorithm outperforms the conventional sliding mode controller (SMC) with the reductions for mean absolute errors of yaw rate and sideslip angle by 43.0% and 37.1% under 0.85 adhesion ratio; with 25.3% and 23.2% reductions under 0.40 adhesion ratio. Therefore, the proposed MRAC controller algorithm improves the vehicle lateral stability and safety.