In the title organic-inorganic hybrid compound, (C(4)H(10)NO)(3)[H(6)CrMo(6)O(24)]·4H(2)O, the Anderson-type [H(6)CrMo(6)O(24)](3-) polyoxoanion is centrosymmetric, with the Cr(III) ion lying on an inversion center. One of the two crystallographiclly independent morpholinium cations is half-occupied. Inter-molecular N-H⋯O and O-H⋯O hydrogen bonds link the cations, polyoxoanions and uncoordinated water mol-ecules.