A rhodium catalyst containing supported rhodium metal omnipresent in the surface layer or in the neighborhood of the surface layer of the particles of a silica or titania type support is presented. This catalyst is prepared by a method (i) in which the support is dipped into an aqueous solution of a water-soluble rhodium salt previously adjusted to a pH of at least 10, followed by the drying and reduction, or a method (ii) in which the support is first dipped into an aqueous solution of a water-soluble rhodium salt having a pH of 1 or less and, then, dipped into an aqueous alkaline solution containing an alkaline compound in an amount sufficient to neutralize the acid impregnated in the support and also sufficient to convert the rhodium salt impregnated in the support into rhodium hydroxide, followed by the drying and reduction.