Connecting three zigzag graphene nanoribbons(ZGNRs) together through the sp~3 hybrid bonds forms a star-like ZGNR(S-ZGNR). Its band structure shows that there are four edge states at k = 0.5, in which the three electrons distribute at three outside edge sites, and the last electron is shared equally(50%) by two sites near the central site. The lowest conductance step in the valley is 2, two times higher than that of monolayer ZGNR(M-ZGNR). Furthermore, in one quasithree-dimensional hexagonal lattice built, both of the Dirac points and the zero-energy states appear in the band structure along the z-axis for the fixed zero k-point in the x-y plane. In addition, it is an insulator in the x-y plane due to band gap 4 eV, however, for any k-point in the x-y plane the zero-energy states always exist at k_z = 0.5. Its band structure shows that there are four edge states at k = 0.5, in which the three electrons distribute at (ZGNRs) together through the sp ~ 3 hybrid bonds forms a star-like ZGNR (S-ZGNR) The lowest conductance step in the valley is 2, two times higher than that of monolayer ZGNR (M-ZGNR). Furthermore, in one quasithree-dimensional hexagonal lattice built, both of the Dirac points and the zero-energy states appear in the band structure along the z-axis for the fixed zero k-point in the xy plane. the xy plane due to band gap 4 eV, however, for any k-point in the xy plane the zero-energy states always exist at k_z = 0.5.