A composite oxide with a high oxygen storage capacity is provided without using cerium. The composite oxide is an iron oxide-zirconia composite oxide containing iron, zirconium, and a rare-earth element. The total content of Fe2O3, ZrO2, and an oxide of the rare-earth element is not less than 90 mass %, the content of an iron oxide in terms of Fe2O3 is 10 to 90 mass %, and the absolute value of the covariance COV(Fe, Zr+X) of the composite oxide, which has been baked in the atmosphere at a temperature of greater than or equal to 900° C. for 5 hours or more, is not greater than 20.