To stabilize the arc bright point position of a discharge lamp and suppress deformation of an electrode when an ultrahigh-pressure discharge lamp with mercury amount above 0.20mg/mm3 is operated with extremely low electric power, the lamp is operated by supplying power from a power supply device having a step-down chopper circuit and a full bridge circuit, a rectangular wave alternating current being supplied when it is operated with rated power or dimmed power (about 60 to 80% of rated power), a DC current being supplied during standby power operation of at most 0.5P (W) with respect to the maximum operating power P (W). Moreover, the high-pressure discharge lamp light source device may be mounted on a projector for projecting images and the mode being changed to standby power operation when there is no change in an image signal, for example, for a prescribed period of time.