A catalyst for use in a process for purifying exhaust gas from a gasoline engine of the fuel-direct-injection type that varies, in response to changes in the air-fuel ratio, between a first exhaust-gas state featured by an air-fuel ratio in the vicinity of the stoichiometrical air-fuel ratio, and a second exhaust-gas state that forms a more oxidizing, low-temperature atmosphere and that is featured by an air-fuel ratio greater than the stoichiometrical air-fuel ratio, the catalyst being obtained by causing a noble metal and a rare-earth oxide and/or a transition metal to be carried by or to be mixed with a fire-resistant inorganic oxide.