The reversal windshield wiper system is a system that realizes the back-and-forth motion of the arms by reversing rotation direction of the motor. In this system, the wiper motor control has to control the reversal angle to meet the regulations that defines the wiping range of the wiper arms and to prevent collision between the wiper arms and the windshield frame. However, the control is often disturbed by the condition of rainfall, deterioration of the wiper blade, fluctuations of the battery voltage, etc. In order to compensate the influence of the disturbances and control the reversal angle of the arms precisely, this paper proposes the motor control and its design method to drive the wiper arms. The control mainly comprises the blocks of motor speed control and target motor speed set. The motor speed control is a state feedback controller and designed by an optimal regulator. The target motor speed set includes the manipulation direction set block that decides the appropriate reversal timing of the target motor speed. The reversal timing is decided based on the predicted motor angle calculated from the wiper system model and it is the most important feature of the control. The effectiveness of the control is demonstrated by experimental results with a wiper test rig.