A method for diagnosing a degree of deterioration of a catalyst, said catalyst being 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, contained in an exhaust gas from said internal combustion engine, said method comprising the steps of: a) intentionally generating and introducing into said catalyst a diagnosis-gas atmosphere containing a target gas higher in concentration than said target gas during a steady-operation state of said internal combustion engine and detecting the concentration of a target gas downstream from said catalyst in said exhaust path; and b) determining whether deterioration exceeding an acceptable level of said catalyst occurs or not by comparing said concentration of the target gas detected in said step a) with a threshold value corresponding to the temperature of said catalyst at the timing which said diagnosis-gas atmosphere is introduced, wherein when the concentration of said target gas in the vicinity on an upstream side of said catalyst in said exhaust path is denoted by Nu, the concentration of said target gas in the vicinity on a downstream side of said catalyst in said exhaust path is denoted by Nl, and a conversion rate defined by the following calculation formula is used as an index representing the degree of oxidation or adsorption occurring in said catalyst, Conversion rate % = 100 × Nu − Nl / Nu, an allowable conversion rate range being a range of said conversion rate allowable in said catalyst is previously defined according to a possible temperature of said catalyst, a value of said Nl with respect to the possible temperature of said catalyst, which is calculated by substituting, into said calculation formula, a lower limit value of said allowable conversion rate range at the temperature as said conversion rate, and an upper limit value of a range of an upstream gas concentration during diagnosis being a possible concentration range of said diagnosis-gas atmosphere in the vicinity on an upstream side of said catalyst as said Nu, is defined as said threshold value. a) intentionally generating and introducing into said catalyst a diagnosis-gas atmosphere containing a target gas higher in concentration than said target gas during a steady-operation state of said internal combustion engine and detecting the concentration of a target gas downstream from said catalyst in said exhaust path; and b) determining whether deterioration exceeding an acceptable level of said catalyst occurs or not by comparing said concentration of the target gas detected in said step a) with a threshold value corresponding to the temperature of said catalyst at the timing which said diagnosis-gas atmosphere is introduced, an allowable conversion rate range being a range of said conversion rate allowable in said catalyst is previously defined according to a possible temperature of said catalyst, a value of said Nl with respect to the possible temperature of said catalyst, which is calculated by substituting, into said calculation formula, a lower limit value of said allowable conversion rate range at the temperature as said conversion rate, and an upper limit value of a range of an upstream gas concentration during diagnosis being a possible concentration range of said diagnosis-gas atmosphere in the vicinity on an upstream side of said catalyst as said Nu, is defined as said threshold value.