Provided are a rinse-off, non-dyeing type hair cosmetic composition containing (a) a polycarboxylic acid or salt thereof, (b) a hydroxymonocarboxylic acid or salt thereof, and (c) an organic solvent selected from aromatic alcohols, alkylene carbonates and polyols at a weight ratio satisfying 0.33 ≤ [(a)+(b)]/(c) ≤ 2.5, in which, the weight of each of (a) and (b) is that as an acid, and the composition has a pH at 25°C of from 2.5 to 5 when diluted to 20 times the weight with water and a method of treating hair, which contains using two hair cosmetic compositions A and B and treating the hair in the order of A → B or B → A and a hair quality improving cosmetic set which contains the hair cosmetic compositions A and B:A: Composition containing Components (a) and (c) at a weight ratio of (a)/(c) = 0.6 or greaterB: Composition containing Components (b) and (c) at a weight ratio of (b)/(c) = 0.25 or greater.The hair cosmetic composition and method of treating hair according to the invention have excellent effects for improving the elasticity and suppleness of the hair and give good feeling upon use during the treatment.
