A ZnO--Pd composite catalyst wherein Pd is dispersed and fixed on the surface of ZnO is produced by ion adsorption process having the steps of soaking ZnO in an acid solution of Pd to adsorb Pd ions (Pd.sup.2+) onto the surface of ZnO; and reducing the adsorbed Pd ions to metallic Pd particles so that the metallic Pd particles are substantially evenly deposited on the surface of ZnO. The ZnO--Pd composite catalyst provides a stable and continuing CO oxidizing capability, without light irradiation, even when the air to be treated contains sulfur compounds such as H.sub.2 S and SOx.