Up to now, almost all many-body theoretical calculations on the ground state of atoms took the Hartree-Fock (HF) model as zeroth order approximation. In this paper, zeroth order Hamiltonian is taken to be Hartree-Fock-Slater (HFS) type, in the double excitation approximation, many-body calculation on the ground state exchangecorrelation energy of beryllium atom is made, the result is in good agreement with experiments and other many-body theoretical calculations, which take HF model as zeroth order approximation. Our calculation shows that, take the HFS model as zeroth order approximation instead, successful many-body calculation on the ground state property of closed shell atoms can also be made.