As an attempts at the electronic structure calculations of the B-type model-DNA, (poly-(guanine) poly-(cytosine)) double helix including sodium atoms as counter cation, hereafter referred as (poly-(dG)poly-(dC), double helix model polymer is performed by means of ab initio Hartree-Fock crystal orbital method adapting the screw axis-symmetry which results in great reduction of computational efforts. All sugar backbones and ions are included in the calculations. Energy band structures are calculated at 3-21G and 6-31G levels. It is significant that the bottom of the lowest conduction band at the Γ point of the first Brillouin zone has almost zero energy value. The effective masses of the hole and electron at the Γ point is 13.7 and 9.53. Both values are relatively large, therefore, the band conductions are expected not to be effective in this model-DNA backbone.