PROBLEMThe present invention is directed to provide a catalyst for purifying exhaust gas capable of maintaining a superior catalytic performance even when the catalyst is exposed to an exhaust gas at a high temperature of 800° C. or higher.SOLUTIONThe catalyst for purifying exhaust gas of the present invention comprises a catalytically active component containing a noble metal and a promoter containing an oxygen storage material both being supported on a carrier. The oxygen storage material comprises cerium, zirconium, and iron, and content of iron in the oxygen storage material is 0.01% by mass or more and less than 0.70% by mass (Fe2O3 conversion) relative to the total mass of the oxygen storage material. And the oxygen storage material is (a) a complex oxide or a solid solution of iron and a metal comprising cerium and zirconium; or (b) an iron is supported on a complex oxide or a solid solution of a metal comprising cerium and zirconium.