We propose and demonstrate numerically a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model, employing the Suzuki-Kubo mean-field Ising dynamics (supplemented by a modified Thouless-Anderson-Palmer reaction field). The resultant dynamics, starting from any arbitrary paramagnetic phase (with local magnetizations mi=±1, for the ith spin, and the global magnetization m=0), takes the system quickly to an appropriate state with small local values of magnetization (mi) commensurate with the (frustrated) interactions. As the temperature decreases with the annealing, the configuration practically remains (in an effective adiabatic way) close to a low-energy configuration as the magnitudes of mi’s and the spin glass order parameter q grow to unity. While the configuration reached by the procedure is not the ground state, for an N-spin SK model (with N up to 10 000), the deviation in the energy per spin EN0-E0 found by the annealing procedure scales as N-2/3, with E0=-0.7629±0.0002, suggesting that in the thermodynamic limit the energy per spin of the low-energy configurations converges to the ground state of the SK model (analytical estimate being E0=-0.7631667265 »), fluctuation σN in EN0 decreases as ∼N-3/4, and the annealing time τN∼N, making this protocol highly efficient in estimating the ground state energy of the SK model.