A non-oxidative hair dye composition containing the components (a) and (b): (a) one or two or more kinds of a glycylglycine derivative represented by the following formula (1) and having two or three amino acid residues or salts thereof, and wherein Y represents an amino acid residue or a bivalent group represented by the formula (2); and (b) a direct dye; Wherein symbol * and R, X, n and m are defined in the claims and in the disclosure.