The dimension-six {ital CP}-violating operator {ital f}{sub {ital a}{ital b}{ital c}{tilde G}} {sup {ital a}}{sub {mu}}{sup {nu}}{ital G{ital b}}{sub {nu}}{sup {rho}}{ital G{ital c}}{sub {rho}}{sup {mu}}, recently proposed by Weinberg as the dominant contribution to the neutron electric dipole moment {ital d}{sub {ital n}}, cannot be supersymmetrized but will occur in the low-energy effective Lagrangian when supersymmetry is spontaneously broken. However, the dimension-five quark electric dipole moment and the quark color electric dipole moment operators contribute to {ital d}{sub {ital n}} even at one loop and become the dominant contributions, though the Weinberg contribution is still quite large.