A control apparatus for speedily warming up a catalyst disposed within an exhaust pipe connected to an internal combustion engine. The control apparatus calculates a demand fuel injection quantity into the engine on the basis of an operating state of said engine, and corrects the calculated demand fuel injection quantity on the basis of a warming-up state of a catalyst provided in an exhaust pipe of the engine so that an air fuel ratio in the engine is repeatedly controlled to a rich side and a lean side in a state that the warming-up of the catalyst is not completed. The control apparatus is equipped with an inhibiting function to inhibit the air fuel ratio from being controlled to the rich side and the lean side when the engine takes an operating state that the injection quantity is set to a rich side with respect to the theoretical air fuel ratio.