Provided is a cleansing composition for skin or hair capable of bringing about a good rinse feel and durability of foam and, in regard to hair, imparting finger combability during rinsing as well as softness to hair during rinsing and after towel drying, and further, imparting a sufficient moist feeling also to skin after application. A cleansing composition for skin or hair, comprising the following (A) and (B): (A) an internal olefin sulfonate having 12 or more and 24 or less carbon atoms; and (B) a cationic polymer or an amphoteric polymer.