A hair care composition, and more particularly, a hair straightening or hair styling composition comprising (A) at least one α or β - hydroxy ketone, (B) a first polymeric compound selected from: (i) at least one hybrid graft polymer derived from (a) a functionalized or unfunctionalized cellulose moiety and (b) at least one functionalized or unfunctionalized acryloyl moiety; or (ii) at least one hybrid graft polymer derived from (a) a functionalized or unfunctionalized galactomannan moiety and (b) at least one functionalized or unfunctionalized acryloyl moiety; (C) at least one organic or inorganic base; (D) optionally, at least one functional polymer; and (E) at least one carrier is provided. Further, disclosed is a process for preparing the hair straightening or hair styling composition and method of hair straightening or hair styling.