In this paper, the asymmetric nuclear matter is studied within the framework of Hartree-Fock approximation with the B3Y-Fetal interaction, a new M3Y-type effective nucleon-nucleon interaction based on the lowest order constrained variational approach (LOCV). This study has been carried out to ascertain and validate the viability of the new effective interaction. For comparative purposes, the famous M3Y-Paris and M3Y-Reid effective interactions are used in this study. The B3Y-Fetal has been used in our previous work in its various density-dependent versions to successfully reproduce the saturation properties of the cold symmetric nuclear matter at the saturation density, ρ = 0.17fm-3. It has been used herein in its DDM3Y1, BDM3Y0 and BDM3Y1 density dependent versions to compute the binding energy per nucleon, also called equation of state (EOS), incompressibility and pressure of asymmetric nuclear matter with results that have proven to be acceptably in agreement with previous work done with the M3Y-Paris and M3Y-Reid by other researchers.