A radiation fan driving apparatus aims to allow a non-stop power supply system to output electric power to drive a radiation fan to continuously rotate at a lower speed to perform heat dissipation even the power supply device is electrically connected to an external electric power source. A control circuit and isolation protective elements are provided so that when the main power source of a computer host is ON, the power supply device delivers electric power through the main power system or the control circuit to the radiation fan to rotate at high speed to provide optimal heat dissipation effect.