A high pressure discharge lamp lighting apparatus that comprises a power supply apparatus that supplies a rectangle wave alternating current to the high pressure discharge lamp for lighting, such that when the lamp is operated by electric power of 0.5×P (W) or less, when maximum operation power P (W) in a steady lighting state except an initial lighting period that is immediately after starting, where a first polarity driving period of a rectangle wave alternating current is Ta (seconds), and where a second polarity driving period is Tb (seconds) an operation is performed so that the second polarity driving period Tb is 5 ms or less (Tb≦5 ms) and a ratio Tb/Ta of these two driving periods is 0.1 or less (Tb/Ta≦0.1).