Spin relaxation due to the D'yakonov-Perel' mechanism is intimately related with the spin splitting of the electronic states. We determine the spin relaxation rates from anisotropic spin splittings of electron subbands in n-(001) zinc blende semiconductor quantum structures calculated self-consistently in the multiband envelope function approach. The giant anisotropy of spin relaxation rates found for different spin components in the (001) plane can be ascribed to the interplay between the bulk and quantum well inversion asymmetry. One of the in-plane relaxation rates may exhibit a striking nonmonotonous dependence on the carrier density.