A correlated ground state of 16O and an E2 giant resonance built on it are calculated using an extended version of the time-dependent Hartree-Fock theory called the time-dependent density-matrix (TDDM) theory. The Skyrme III force is used as an effective interaction for the calculation of both a mean field and two-body correlations. It is found that a TDDM calculation with the Skyrme force gives reasonable ground-state correlations and a large spreading width of the E2 giant resonance.