A topical skin composition containing a dipeptide compound represented by formula (1) or a salt of the dipeptide: ##STR00001## wherein R.sup.1 represents a hydrogen atom, an alkyl group, an alkanoyl group, or --CH(R.sup.6)COOR.sup.7 (wherein R.sup.6 represents a hydrogen atom or a lower alkyl group, and R.sup.7 represents a hydrogen atom, a lower alkyl group, a lower alkenyl group, or an aralkyl group); R.sup.2 represents a hydrogen atom or an alkyl group which may have a substituent; R.sup.3 represents a lower alkyl group or a phenyl group; R.sup.4 represents a hydrogen atom or a lower alkyl group, and may form a heterocyclic ring together with R.sup.5 and an adjacent nitrogen atom; R.sup.5 represents a hydrogen atom, an alkyl group which may have a substituent, or an aralkyl group which may have a substituent, and may form the heterocyclic ring together with R.sup.4; X represents --COOR.sup.8 (wherein R.sup.8 represents a hydrogen atom, a lower alkyl group, a lower alkenyl group, or an aralkyl group) or --SO.sub.3H; and n is an integer of 0-4; and a pharmaceutically acceptable carrier therefor.