Provided is a cleansing composition for skin or hair which can provide a good rinse feel and can enhance the combing property of hair after rinsing and the manageability after drying in application to the hair and can impart a sufficient moist feeling to skin in application to the skin.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) an oil solution having a solubility of from 0 to 1 g in 100 g of water at 20° C.