A motor-driving control system includes an actuator configured to generate rotational force by driving received current, a current provider configured to provide current to the actuator while repeatedly turning on and off the current at a preset period and duty, and a controller configured to estimate a rotation position or a rotation speed of the actuator in a section in which the current of the current provider is turned on or off and to control the current provider to follow a speed command based on the estimated rotation position or rotation speed.