[Purposes] This paper aims to solve the problem of saturation in terms of output torque amplitude and response speed of hub motors. [Methods] The distributed electric drive vehicle was studied, and the second-order nested saturation function was used for the anti-saturation design of sliding mode control. The upper and lower limit parameters of the anti-saturation sliding mode controller were designed based on the peak torque of the hub motor and the actual response of the hub motor in the bench experiment. [Findings] The anti-saturation sliding mode controller can strictly limit the amplitude and the change rate of direct yaw moment， and greatly improve the lateral stability of the vehicle under extreme working conditions. [Conclusions] The proposed method effectively solves the problem that the hub motor is easy to fall into saturation under extreme working conditions， and avoids the instability of the vehicle due to wheel slip.