A purifying catalyst for the exhaust gas from the internal combustion engine of an automobile, for example, is disclosed which excels in the purifying ability in quick response to the atmosphere of the exhaust gas largely varying with changes in the operating condition of the engine involving such phases as idling, acceleration, constant-speed drive, and deceleration. The purifying catalyst contains rhodium, palladium, a cerium compound, and a refractory inorganic oxide as catalytic components carried on a refractory carrier and comprises at least two catalyst layers, namely a catalyst layer containing the cerium compound and a catalyst layer containing palladium.