To provide: a production method using a catalyst which can substantially suppress leaching of active metal components and exhibit high activity for both reactions of transesterification of glycerides and esterification of free fatty acids each contained in a fat or oil; and the catalyst. A method for producing fatty acid alkyl esters and/or glycerin comprising a step of bringing a fat or oil into contact with an alcohol in the presence of a catalyst, wherein the catalyst is at least one catalyst selected from the group consisting of the following (I) to (V): (I) a metal oxide having an ilmenite structure and/or a slyrankite structure; (II) an oxide containing a metallic element belonging to the Group 12 and a metallic element belonging to the Group 4; (III) a mixed oxide containing a metallic element belonging to the Group 12 and a tetravalent transition metallic element; (IV) a metal oxide containing zirconium and at least one metallic element selected from the group consisting of metallic elements belonging to the Groups 4, 5 and 8; and (V) a metal oxide containing anatase type titanium oxide and/or rutile type titanium oxide, and the metal oxide containing a sulfur component of 700 ppm or less.