In this paper we have reported the study of symmetry energy within the self-consistent Green-function approach. For the sake of comparison, the same calculations are performed using Brueckner–Hartree–Fock approximation. The symmetry energy is calculated for different densities and discussed in comparison with other predictions. The self-consistent Green’s function leads to slightly larger energies as compared to the Brueckner–Hartree–Fock approach. This effect increases with density and thereby leads to smaller symmetry energies. The calculation of the symmetry energy in the Brueckner–Hartree–Fock approach shows a monotonic increase as a function of baryonic density. We extract the symmetry energy coefficient at density 0.16 fm-3 to be about 28.3MeV for self-consistent Green-function approach using CD-Bonn potential, which is in good agreement with the empirical value of 30 +/- 4 MeV. The dependence of the equation of state on the neutron excess parameter is clearly linear as function of alpha for self-consistent Green-function approach.