Provided is a discharge lamp lighting device, which can control a load precisely while improving the practicability. When the difference of a count number (Nn) becomes a predetermined threshold value or less, a predictor circuit (35) predicts the timing, at which a current value (iQ1) becomes a peak value, on the basis of the rate of change of the difference. A switch selecting circuit (38), which is driven with a clock frequency higher than the sampling frequency of a first converter unit (32), turns off a field effect transistor (Q1) at the turn-off timing, and turns on a field effect transistor (Q2). A plurality of A/D converters (37a) are subjected to a multi-rate control, thereby to correct the threshold value of the predictor circuit (35) on the basis of the peak value of a lamp current (iOUT). Even if the peak values of current values (iQ1 and iQ2) are positioned for the sampling period of the first converter unit (32), the turn-off timings can be precisely set according to the current values (iQ1 and iQ2) without increasing the sampling frequency more than the necessary value. As a result, it is possible to improve the practicability and to control the lighting of a fluorescent lamp precisely.