There is provided a method for preparing a sulfone or sulfoxide compound, characterized
in that a sulfide compound is allowed to react with hydrogen peroxide in the presence
of a metal oxide catalyst formed by the reaction of hydrogen peroxide with at least
one metal or metal compound selected from tungsten metal; molybdenum metal; a tungsten
compound comprising tungsten and a Group IIIb, IVb, Vb, or VIb element exclusive
of oxygen; and a molybdenum compound comprising molybdenum and a Group IIIb, IVb,
Vb, or VIb element exclusive of oxygen.