A method for diagnosing the degree of deterioration of a catalyst disposed in an exhaust path of an internal combustion engine and oxidizes or adsorbs a target gas, including at least one of a hydrocarbon gas and a carbon monoxide gas in an exhaust gas from the internal combustion engine, is adapted to determine whether deterioration exceeding an acceptable level of a catalyst occurs or not by comparing the concentration of a target gas detected downstream from the catalyst in the exhaust path when a diagnosis-gas atmosphere containing a target gas higher in concentration than a target gas during a steady-operation state of the internal combustion engine is intentionally produced and introduced into the catalyst with a threshold value corresponding to the temperature of a catalyst at the timing which the diagnosis-gas atmosphere is introduced.