There is provided a cleansing composition for skin or hair which can provide a good durability of foam and rinse feel, enhance combing property of the hair during rinsing to impart softness to the hair, and impart a refreshing feeling upon application to the skin without causing stickiness. A cleansing composition for skin or hair contains the following (A) and (B): (A) an internal olefin sulfonate having 12 or more and 24 or less carbon atoms; and (B) an anionic surfactant having no sulfate group except the internal olefin sulfonate (A) and an anionic surfactant having two or more carboxylic acid groups.