A topical skin composition containing a dipeptide compound represented by, formula (1) or a salt of the dipeptide: wherein R1 represents a, hydrogen atom, an alkyl group, an alkanoyl group, or —CH(R6)COOR7 (wherein R6 represents a hydrogen atom or a lower alkyl group, and R7 represents a hydrogen atom, a lower alkyl group, a lower alkenyl group, or an aralkyl group); R2 represents a hydrogen atom or an alkyl group which may have a substituent; R3 represents a lower alkyl group or a phenyl group; R4 represents a hydrogen atom or a lower alkyl group, and may form a heterocyclic ring together with R5 and an adjacent nitrogen atom; R5 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 R4; X represents —COOR8 (wherein R8 represents a hydrogen atom, a lower alkyl group, a lower alkenyl group, or an aralkyl group) or —SO3H; and n is an integer of 0-4; and a pharmaceutically acceptable carrier therefor.