To provide an oxidation catalyst desulfurizing apparatus and a method that can upgrade fuel consumption, alleviate emission of harmful exhaust gas amount, and minimize irreversible deterioration reaction of an oxidation catalyst.

This oxidation catalyst desulfurization apparatus includes: an engine 100; an oxidation catalyst 200 that purifies the harmful material contained in an exhausted gas; a temperature detection part 210 that detects the temperature at the front end of the oxidation catalyst; and a control part 300 that accumulates the time or distance wherein natural desulfurization occurs from the temperature at the front end of the oxidation catalyst, reflects the accumulated natural desulfurization occurrence time or distance in a set desulfurization operation time or a set desulfurization cycle, and carries out desulfurization operation of the oxidation catalyst. The control part calculates the cumulative time or distance, which exceeds the desulfurization temperature with a set temperature at the front end of the oxidation catalyst with the natural desulfurization occurrence time or the natural desulfurization occurrence distance.