Some technology is known in which the ignition timing is corrected toward the retard side so as to increase an exhaust gas temperature and thereby promote an activation of catalyst during an idling operation after a cold start of an internal combustion engine. For example, in Patent Literature 1, retard amount and retard-correcting period for the ignition timing are set based on a temperature of cooling water during the idling operation generated after the cold start. Specifically, in order to promote temperature rise of the exhaust gas, the retard amount is set at a larger value as an engine-start-time temperature of the cooling water becomes lower. Moreover, the retard-correcting period is set at a larger value as the engine-start-time temperature of the cooling water becomes lower.