To prepare the subject composition providing low stimulation, hardly causing squeaky feeling when shampooing or rinsing hair and capable of manifesting excellent conditioning effect after shampooing the hair by using a specific N-acylamino acid in combination with specified different kinds of cationic polymers.

This hair shampoo composition contains (A) an N-acyl acidic amino acid salt or an N-acyl neutral amino acid salt, (B) a cationized cellulose of formula I {Z is H or a group of formula II [R3 is an 8-22C (branched) alkyl or alkenyl; R1 and R2 are each H or R3]; (x) is 10-3,000; (y) is 1-10}, (C) a cationized polymer without the component B {e.g. chlorinated O-[2- hydroxy-3-(trimethylammonio)propyl]hydroxyethyl cellulose and a cationized gum guaiac}, and optionally (D) a surfactant of a compound of formula III [R4 is R3; M1 is H or an alkali (alkaline earth) metal; (p) is 1-3].