A cleaning composition for a semiconductor substrate contains a solvent, and a polymer that includes a fluorine atom, a silicon atom or a combination thereof. The content of water in the solvent is preferably no greater than 20% by mass. The cleaning composition preferably further contains an organic acid which is a non-polymeric acid. The organic acid is preferably a polyhydric carboxylic acid. The acid dissociation constant of the polymer is preferably less than that of the organic acid. The solubility of the organic acid in water at 25° C. is preferably no less than 5% by mass. The organic acid is preferably a solid at 25° C.