A high pressure discharge lamp lighting device can prevent the deformation of electrodes by stabilizing an arc start position of a discharge lamp under the condition of low-power operation of a high pressure discharge lamp with a mercury seal volume of 0.20mg/mm3. A lighting device which has a buck circuit (1) and a full-bridge circuit (2) can supply power to the high pressure discharge lamp (10) so as to lighten the high pressure discharge lamp. Under the condition of lightening with a rated power or a dimming power (which is about 60 to 80% of the rated power), a rectangle wave alternating current is supplied to the discharge lamp (10) for lighting. Besides, the high pressure discharge lamp can be lightened by supplying an asymmetrical rectangular wave alternated current in a driving period when the lamp is operated by electric power of 0.5P (W) or less, the maximum operation power P (W) in a steady lighting state except an initial lighting period is immediately after starting, a first polarity driving period of a rectangle wave alternating current is Ta (seconds), a second polarity driving period is Tb (seconds), the second polarity driving period Tb is 5 ms or less (Tb is less than or equal to 5 ms) and a ratio Tb/Ta of these two driving periods is 0.1 or less (Tb/Ta is less than or equal to 0.1).