To eliminate the disadvantage that the lamp current becomes large in a light source device with a discharge lamp with high radiance in a lamp with a low saturation lamp voltage, in a light source device having a discharge lamp with a pair of opposed electrodes connected to a feed device which starts the discharge lamp and which is used to supply the discharge current to the electrodes, the feed device is made to control the current feed such that the current flowing in the discharge lamp does not exceed a given current boundary value, such that, during the interval immediately after starting of the discharge lamp until sufficient heating of the discharge lamp is achieved, the current boundary value is a first boundary value, and that, after the interval expires, the current boundary value is changed to a second boundary value that is smaller than the first boundary value.