A system and method for detecting a failure occurring in an exhaust secondary air supply system of an internal combustion engine. A conduit is connected to the exhaust pipe to supply secondary air to the exhaust pipe to promote oxidization of the emissions in the exhaust gases. A valve is provided in the conduit for opening/closing it. The failure of the valve is detected by operating the air pump to supply the air in the conduit, while closing the conduit by the valve. The air/fuel ratio is detected by an oxygen sensor installed downstream of the conduit to be compared with a desired air/fuel ratio. If the detected air/fuel ratio is leaner than a desired air/fuel ratio, the air flows to the exhaust pipe so that the valve is considered to be stuck to open. Alternatively, a pump current is detected and is compared with a reference value indicative of the current at no air flow. If the detected current is less than the reference value, the valve is considered to be in failure. Moreover, the movement of a valve member is sensed to detect whether the valve is stuck to close.