An ion beam processing apparatus and a method of operating an ion source therefor are provided for reducing the frequency of breakdown due to particles, and for increasing an apparatus available time by operating the apparatus in a stable state for a long time and minimizing maintenance operations such as cleaning for the apparatus, and so on. A plasma generating gas is introduced into a vacuum chamber formed of a processing chamber and an ion source mounted thereto to produce a plasma from the gas, and an electric field is applied within the vacuum chamber to extract ions within the plasma as an ion beam. The ion source comprises an arc power supply, an acceleration power supply for applying an acceleration electrode with a positive potential to extract an ion beam, and a deceleration power supply for applying a deceleration electrode with a negative potential to prevent ions from flowing into the ion source. When the ion source is operated, the acceleration electrode is first applied with the positive potential, and then the deceleration electrode is applied with the negative potential.