A leave-on hair cosmetic composition, which contains the following components (A) and (B): (A) an organic C2-8 dicarboxylic acid or salt thereof, and (B) at least one or more of an organic solvent selected from the group consisting of aromatic alcohols, N-alkylpyrrolidones, alkylene carbonates, polypropylene glycols, lactones and cyclic ketones, wherein the organic solvent has a ClogP of from −2 to 3; and wherein the cosmetic composition has a pH of from 2 to 5 at 25° C. when diluted to 20 times its weight with water and has a buffering capacity of 0.001 gram equivalent/L or greater but less than 0.2 gram equivalent/L. A hair quality improving method which comprises treating the hair with the hair cosmetic composition. This hair cosmetic composition provides benefits such as enhancement of luster, manageability, pliability and elasticity of dry hair to which it is applied, such as hair dehydrated and damaged by coloring, permanent waving, or repetitive excessive blow drying.