An object of the present invention is to provide a catalyst exhibiting excellent performance particularly in partial oxidation reaction. Another object is to provide a method for efficiently producing carboxylic acid or carboxylic anhydride through vapor-phase partial oxidation of an organic compound by use of an oxygen-containing gas in the presence of the catalyst. The catalyst contains (1) diamond; (2) at least one species selected from among Group 5 transition element oxides, collectively called oxide A; and (3) at least one species selected from among Group 4 transition element oxides, collectively called oxide B. The method for producing a carboxylic acid or a carboxylic anhydride includes subjecting an organic compound to vapor phase partial oxidation by use of an oxygen-containing gas in the presence of the catalyst, wherein the organic compound is an aromatic compound having one or more substituents in a molecule thereof, the substituents each including a carbon atom bonded to an aromatic ring.