The present invention relates to a discharge lamp driver, a light source device, a projector, and a method of driving a discharge lamp by which the inter-electrode distance of the discharge lamp becomes very small. On the condition that an inter-electrode voltage is smaller than a first predetermined value, a control unit controls a discharge lamp control part in a manner of setting a hybrid period and a third period, during the hybrid period, a first period for supplying an AC current to the discharge lamp and a second period for supplying a DC current to the discharge lamp are alternately repeated, and the third period alternately includes a first direct-current period for supplying the DC current to the discharge lamp and a second direct-current period for supplying a DC current havingthe polarity reverse with the polarity of the DC current supplied to the discharge lamp during the first DC period. The length of the first direct-current period is larger than the length of the second direct-current period. The length of the second direct-current period is smaller than 0.5 ms. A total of the lengths of the first direct-current periods in the third period is larger than a length of the second period. When the inter-electrode voltage is smaller than the first predetermined value, the control unit is configured to increase the length of the third period in a stepwise manner.