This invention relates to a cosmetic composition, in particular a composition in the form of cream or lotion, for make-up removal and a textile product, in particular a wipe, soaked in such a composition. In particular, this invention relates to a make-up remover composition in the form of oil-in-water emulsion containing: a) at least one hydrocarbon with C13-C30 chain, b) an oily component comprising at least one ester of a fatty alcohol, c) at least one alcohol with C12-C24 chain, d) cetearyl glucoside.