Removal of poisoning substance (sulfur oxidant) is controlled based upon estimating an amount of the poisoning substance deposited in an exhaust gas purification catalyst disposed in an exhaust pipe for an internal combustion engine, a lower limit is set corresponding to a possible removal amount of the poisoning substance varying with a state of a catalyst, and the removal control of the poisoning substance is ended when the estimated amount is less than the lower limit. The estimated amount can be accurately calculated, thereby ending the removal control at a proper timing. Fuel economy and exhaust gas purification performance improves.