In the present paper, density functional theory calculations have been implemented by using Dmol3 to study the electronic band structures of β-graphyne nanotubes (βGyNTs) and γ-graphyne nanotubes (γGyNTs). Our results found different GyNTs show diverse electronic band structures. All βGyNTs have quite small band gaps without any correlation with tube size. Meanwhile, γGyNTs, no matter zigzag or armchair, exhibit semiconductor characteristics with oscillatory band gap ranging from 0.48 eV to 1.20 eV. Furthermore, based on the variation of band gap, both zigzag and armchair γGyNTs can be divided into two subgroups: 2m and 2m + 1 where n is a positive integer, following the order of 2m + 1 > 2m.
