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A new control strategy for obtaining the maximum traction force of electric vehicles with individual rear-wheel drive is presented. A sliding-mode observer is proposed to estimate the wheel slip and vehicle velocity under unknown road conditions by measuring only the wheel speeds. The proposed observer is based on the LuGre dynamic friction model and allows the maximum transmissible torque for each driven wheel to be obtained instantaneously. The maximum torque can be determined at any operating point and road condition, thus avoiding wheel skid. The proposed strategy maximizes the traction force while avoiding tire skid by controlling the torque of each traction motor. Simulation results using a complete vehicle model under different road conditions are presented to validate the proposed strategy.