Connecting three zigzag graphene nanoribbons (ZGNRs) together through the sp3 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 kz =0.5.