A pyrochlore-type oxide represented by a general formula A2B2O7-Z is prepared by precipitate formation, where A and B each represent a metal element, where Z represents a number of at least 0 and at most 1, where A contains at least one element selected from a group consisting of Pb, Sn, and Zn, and where B contains at least one element selected from a group consisting of Ru, W, Mo, Ir, Rh, Mn, Cr, and Re. Impurities are then sufficiently removed through washing and drying processes, and the pyrochlore-type oxide is calcined under controlled conditions. This allows the crystallinity of the pyrochlore-type oxide, which contained amorphous parts immediately after the production of the precipitate, to be increased so that the resistance to acid can be improved while preventing particle aggregation.