Disclosed is a hair dye composition which is excellent in the capability of dyeing (or decoloring) damaged hair, fragile and weakened hair, or naturally fine and soft hair and which can impart bounce, body and volume to hair. Specifically disclosed is a hair dye composition which comprises the following components (a) and (b) and shows a pH value of 2 to 12 upon use: (a) 0.1 to 20 mass% of an aromatic sulfone compound represented by the general formula (1) [wherein R's independently represent a hydrogen atom or a univalent hydrocarbon group, or adjacent two R's together form a saturated or unsaturated bivalent hydrocarbon group； Y represents a hydrogen atom when X represents an oxygen atom, and Y represents a carbonyl group bound to X when X represents a nitrogen atom； an Z
