A control apparatus for an internal combustion engine is provided, the control apparatus being capable of effectively suppressing the inflow of fresh air into a catalyst due to an operational delay of the valve stop mechanism when an execution request for fuel cut is issued. There is provided a valve stop mechanism capable of changing the operational states of intake valves and exhaust valves between a valve operating state and a valve closed/stopped state. The operational states of the intake and exhaust valves are changed into the valve closed/stopped state, if the engine rotational speed decreases to or below a predetermined rotational speed when the engine rotational speed is higher than the predetermined rotational speed in a case where an execution request for fuel cut is detected and the temperature of the catalyst is not lower than a predetermined temperature during operation of an internal combustion engine