A discharge lamp lighting apparatus has a configuration including a control unit which discriminates, for each polarity of an AC rectangular wave output, the output voltage detected with an output voltage detector for detecting the voltage applied to a discharge lamp, and carries out constant power control for each polarity separately. By thus detecting the output voltage for each polarity separately and by outputting a target current for each identical polarity, it can carry out constant power control positively even if the output voltage varies for each polarity, thereby being able to prevent current feedback to a different polarity, and to prevent power oscillation and partial reduction of electrodes due to an increase of the output voltage difference for each polarity.