We start from a realistic nuclear force (N3LO  or JISP16 ), and use the similarity renormalization group (SRG) to renormalize the realistic nuclear force. With the softened NN force, we first perform the Hartree-Fock (HF) calculation, and then take the HF solution as the reference and basis for further corrections to the solution of the many-body system. The many-body perturbation theory (MBPT)  has been employed for the correction calculations. Corrections up to the third order in energy and up to second order in radius have been considered. As preliminary investigations, we have calculated 4He and 16O, obtaining quite good converged results in their binding energies and radii. We thank J. Vary for providing the JISP16 interaction and useful discussions.  D.R. Entem and R. Machleidt, Phys. Rev. C 68, 041001 (32003);  A.M. Shirokov, A.I. Mazur, S/A. Zaytsev, J.P. Vary and T.A. Weber, Phys. Rev. C 70, 044005 (2004);  I. Shavitt and R.J. Bartlett, Many-body methods in Chemistry and physics: MBPT and coupled-cluster theory (2009).