PROBLEM TO BE SOLVED: To provide a composite having fine particle sizes in such a nano level that the particle sizes are 1-20 nm, in which nanoparticles of cerium oxide CeOwhose particle sizes are uniform exist in a dispersed form in zeolite.SOLUTION: A "Linde Q" type zeolite having a composition of KO-AlO-2SiO-xHO and hexagonal plate-like crystal form is dipped into aqueous solution of a soluble salt of Ce, and ion exchange of Kor Naand Ceion in the zeolite is performed at a temperature of &le；100°C, to thereby allow Ce ion to exist in the zeolite with at least 10% exchange rate. The ion exchanger is fired at a temperature of &ge；200°C under an oxidative atmosphere to oxidize cerium (III) into cerium (IV), and thereby this composite in which cerium oxide nanoparticles are dispersed into zeolite is obtained. Further, the cerium oxide nanoparticles can be obtained as a single substance by dissolving and removing the zeolite.
