The invention provides a light source apparatus which suppresses blackening of a discharge lamp and maintaining a constant clearance between the electrodes of the discharge lamp, and a projector that utilizes the light source apparatus and the driving method. The light source apparatus includes the discharge lamp including a light-emitting container, and a pair of electrodes disposed such that a respective tip portion thereof opposes each other in the light-emitting container, and a driving unit that supplies a driving current to the pair of electrodes. The driving unit includes an AC supplier that supplies an alternating current of a frequency not lower than 1 kHz and not higher than 10 GHz to the pair of electrodes and a DC supplier that supplies a direct current to the pair of electrodes. The AC supplier is configured so as to alternately repeat an AC supply section in which the alternating current is supplied and an AC stop section in which the supply of the alternating current is stopped, and the DC supplier is configured so as to supply the direct current during a period corresponding to the AC stop section.