For maintaining the projections of the electrode tip ends in the ideal condition and maintaining a stable arc even if the lamp is lighted with a lamp power of at most 70% of the rated electric power, a high pressure discharge lamp light source device is provided, comprised of a high pressure discharge lamp having a discharge vessel made from quartz glass and a pair of electrodes arranged oppositely to each other with a spacing of at most 2.0 mm, each electrode having a projection formed at a tip end thereof, and mercury of at least 0.20 mg/mm3 and a halogen being enclosed in said discharge vessel; and a power supply device for supplying alternating current to said high pressure discharge lamp, wherein the power supply device is adapted to switch between a nominal electric power lighting mode and a low electric power lighting mode, said current in the low electric power lighting mode having a defined current value in the range of 40 to 70% of a nominal electric power consumption, and wherein said power supply device, in the low electric power lighting mode, is adapted to alternatingly supply to said high pressure discharge lamp a base current having a defined frequency chosen from a range between 100 Hz and 5 kHz and a boost current having a higher current value than a current value of said base current.