To maintain the shape of the projection on the electrodes of the tip end for a long time to extend the lifetime of a discharge lamp, a lighting device lighting a high pressure discharge lamp supplies alternating current such that an alternating current with a basic frequency at the time of the steady state lighting selected from a range between 60 and 1000 Hz and a low frequency of a half cycle with a frequency lower than the basic frequency are generated alternatingly. The alternating current is supplied such that the waveform with one polarity of the low frequency appears consecutively at least twice. It is also possible for the alternately generated low frequency to be lower than the basic frequency in a range from 5 to 200 Hz, and for the interval during which the basic frequency is supplied to be gradually increased and decreased at specified times.