An apparatus for purifying exhaust gas exhausted from an internal combustion engine, using two or more honeycomb structure-type catalysts (X) and (Y). The catalyst (X) contains the support material of the zirconium oxide as a main component which loads a Rh component on the support material of zirconium oxide and substantially does not contain a cerium component, and a cerium-containing oxide which substantially does not load the Rh component, and the catalyst (X) does not substantially contain Pt component and Pd component. The catalyst (Y) contains the support material of the cerium-zirconium composite oxide as a main component which loads a Rh component on the support material of cerium-zirconium composite oxide and which contains cerium of 1 to 20% by weight, in an oxide equivalent, and zirconium of 99 to 80% by weight, in an oxide equivalent, and the catalyst (Y) does not substantially contain Pt component and Pd component.