A system and a method of driving a motor are provided. A zero crossing reference module defines a zero-crossing region based on a current zero-crossing point of a coil of the motor, and a mode switching setting module sets a reference parameter of a back electromotive force when the motor rotates at a preset rotating speed. When the current zero-crossing point fails to fall in the zero-crossing region, a driving mode selector module selects a voltage detection mode. When a parameter of the back electromotive force is equal to the reference parameter, the driving mode selector module selects to switch back to a current detection mode. A motor driving controller module calculates a position of a rotor of the motor based on the current in the current detection mode and determines the position based on the back electromotive force in the voltage detection mode to drive the motor.