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Due to quick response and large quantity of electric motor torque, the traction wheels of battery electric vehicle are easy to slip during the initial phase of starting. In this paper, a sliding mode control approach of acceleration slip regulation is designed to prevent the slip of the traction wheels. The wheel slip ratio is used as the state variable for the formulation of system dynamics model. The fuzzy algorithm is utilized to adjust the switch function of sliding mode controller. After stability and robustness analysis, the sliding mode control law is transferred into C code and downloaded into vehicle control unit, which is validated under wet and dry road conditions. The experimental results with a small overshoot and a quick response during starting indicate that the sliding mode controller has good control effect on the slip ratio regulation. This article proposes an acceleration slip regulation method that improves the safety during acceleration for battery electric vehicle.