The three-body force effects on the equation of state and its iso-spin dependence of asymmetric nuclear matter and on the proton fraction in neutron star matter have been investigated[1] within Brueckner Hartree-Fock (BHF) approach by using a microscopic three-body force. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β=(N-Z)/A is fulfilled in the whole asymmetry range 0 ≤β ≤1 and also up to high density. The three-body force provides a strong enhancement of symmetry energy at high density in agreement with relativistic approaches. Thecalculated proton fraction in β stable neutron star matter is given in Fig.l, where the thick solid line is the BHF prediction using AV18+TBF, while the dotted one is the BHF result using AVis. The thin solid line is the prediction of the Dirac-Brueckner approach taken from Ref.[2]. The results extracted according to the phenomenological paramete rizations of the symmetry energy suggested in Ref.[3] are also plotted. It is seen from