The ball screw actuated by the electric motor is widely used as an essential actuator for driving the mechanical system by virtue of accuracy and force transmission capability. In this paper, a design of the global sliding mode control is presented to drive the ball screw actuator along the minimum time trajectory, In the proposed control scheme, if the ranges of parametric uncertainties and torque limits of the system are specified, the arrival time of the load along the minimum time trajectory can be estimated. Also, the arriving time at the reference input and the maximum acceleration are expressed in a closed form solution. Conversely, the capacity of a ball screw actuator including the motor can be easily designed if the external load and its transportation time are specified. The superior performance of the proposed control scheme and analysis is validated by the computer simulation and experiments comparing with other sliding mode controllers.