A control system is disclosed that accelerates the rise in temperature of a catalyst provided in an exhaust system of an internal combustion engine. The system increases the intake air amount after the engine starts and retards the ignition timing according to a rotational speed of the engine. In this control system, a failure of the catalyst temperature rise acceleration control is diagnosed according to the engine rotational speed and/or a retard amount of the ignition timing during the execution of the catalyst temperature rise acceleration control. The above failure may also be diagnosed according to at least one of the ignition timing and the engine rotational speed when decreasing the intake air amount during the execution of the catalyst temperature rise acceleration control. The above failure may also be diagnosed according to a detected catalyst temperature and an estimated catalyst temperature.