In a chopper circuit, output power is controllable with a direct current power source as a power source, and a smoothing capacitor is connected between output terminals of the chopper circuit. A polarity inversion circuit applies an alternating voltage to a high pressure discharge lamp with a voltage across the smoothing capacitor as a power source. The output power of the chopper circuit and an inversion frequency of the polarity inversion circuit are controlled by a control circuit based upon a terminal voltage of the smoothing capacitor, which is detected by a voltage detecting circuit. In the control circuit, a switch voltage is set for defining a range of voltages detected by the voltage detecting circuit, and the inversion frequency is changed in plural stages according to the magnitude relation between the detected voltage and the switch voltage. The inversion frequency corresponding to electric power applied to the high pressure discharge lamp is set with respect to each range of lamp voltages, to thereby inhibit occurrence of an arc jump.