This invention relates to a catalyst for purifying an exhaust gas using a complex oxide having good heat-resistant and a purification performance which does not undergo degradation, particularly in a lean atmosphere at a high temperature of about 1,000.degree. C., by using the complex oxide containing platinum and at least one member of element selected from the group from an alkaline earth metal element and the Group IIIA element and, furthermore, by using at least one member of platinum complex oxides selected from the group of those Pt complex oxides expressed by the chemical structural formulas X.sub.4 PtO.sub.6 (X=Ca, Sr, Ba, Mg), X'.sub.2 Pt.sub.2 O.sub.7 (X'=Sc, La, Pr), SrX"PtO.sub.6 (X"=Co, Ni, Cu), Ba.sub.2 ZPtO.sub.6 (Z=Pr, Ce) and Ba.sub.8 Y.sub.3 Pt.sub.4 O.sub.17.5.