As an attempt at the electronic structure calculations of the B-type model-DNA, (poly-(guanine) poly-(cytosine)) double helix including sodium atoms as counter cations, 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. At the level of 6-31G basis sets, energy band structures were calculated for the polymers with and without sugar and sodium phosphate and found that the difference is very large when excluding the sodium phosphate. We also calculated the four single helix polymers in order to compare these band structures with the double helix polymononucleotide. The difference is not small especially for the guanine-citosine polymer.