A driving device includes a case with a cover mounted thereto. A transmission device is received in the case and has a stepper motor and a gear reduction unit which includes multiple gears engaged with each other. The stepper motor drives the gear reduction unit which is connected to an object. A circuit board is connected with the transmission device and provides power to the stepper motor and controls the stepper motor. A sensing device has a sensor and a detector which is connected to one of the gears of the gear reduction unit. When the gear reduction unit drives the detector to pass the sensor, the sensor sends a signal to the circuit board which keeps on providing the power to the stepper motor. When no signal is sent to the circuit board by the sensor, the circuit board cuts off the power to the stepper motor.