We introduce a new framework for designing a d-electrons dominant Dirac cone based on the hybridization between the atoms in TM-monolayers(TM = Ti,Zr and Hf) with honeycomb structure by considering the effects of spin–orbit interaction(SOC)and the enhanced electronic correlation.For both standard and beyond approaches,spin polarized Dirac points contributed by d states can be formed in TM-monolayers.With GGA+U,the bond lengths are slightly increase than that with GGA and this elongation may be caused by the bond localization.The on-site coulomb repulsion may weaken the covalency between the TM in monolayer,consequently,elongating the bonds.A simplified analysis on a general 2D system,which contains two atoms of the same species in each unit cell,demonstrated that a hexagonal cell is the most favorable for the existence of Dirac cones.The competed results suggest that largest gap of about 151 meV appearance in Hf-honeycomb by the combined impact of Coulomb interaction and SOC.The Zr-honeycomb has the highest Fermi velocity(3 ? 105 m s-1)and Ti-system has the most prominent feature of spin-polarized.With a large exchange field in these TM-monolayers,the spin splitting induced by SOC may be enhanced through the strong d-d hybridization between the TMs and the on-site Coulomb interaction U also have effects on the contribution of d orbital to Dirac bands.