In a limited-current type gas sensor which detects oxygen-containing gas contained in an exhaust gas of an internal combustion engine, the decomposition current value of water (H2O) may be detected, and existence of an abnormality of output characteristics of the sensor may be diagnosed based on its deviation from a reference decomposition current value of water corresponding to the concentration of water contained in the exhaust gas. A NOx sensor and a SOx sensor can also diagnose remarkable and minute abnormalities of output characteristics. In addition, the reference decomposition current value of water may be acquired based on the concentration of water detected by a separate humidity sensor or the decomposition current value of oxygen detected by the limited-current type gas sensor. The reference decomposition current value of water may be corrected based on a decomposition current value of oxygen detected during a fuel cut.