Controlling an immeasurable state with an indirect control input is a difficult problem faced in traction control of vehicles. Research on motion control of electric vehicles (EVs) has progressed considerably, but traction control has not been so sophisticated and practical because of this difficulty. Therefore, this paper takes advantage of the features of driving motors to estimate the maximum transmissible torque output in real time based on a purely kinematic relationship. An innovative controller that follows the estimated value directly and constrains the torque reference for slip prevention is then proposed. By analysis and comparison with prior control methods, the resulting control design approach is shown to be more effective and more practical, both in simulation and on an experimental EV.