The electronic band structures and total density of states based on a density-functional theory are performed on four deoxyribonucleic acid (DNA) molecules: namely, A- and B-type DNA where a single pitch is formed by 11 and 10 base pairs, respectively, of Poly (dA) *Poly (dT) and Poly (dG) *Poly (dC). Poly (dA) *Poly (dT) is a DNA where one single strand consists only of adenine (A) and the other single strand consists only of thymine (T), while Poly (dG) *Poly (dC) is a DNA where one single strand consists only of guanine (G) and the other of cytosine (C). A- and B-Poly (dA) *Poly (dT) and A- and B-Poly (dG) *Poly (dC) DNA. Compared in the same structure, the band gap of Poly (dA) *Poly (dT) is larger than that of Poly (dG) *Poly (dC). The highest occupied molecular orbitals (HOMO's) of Poly (dA) *Poly (dT) and Poly (dG) *Poly (dC) are formed by adenine's and guanine's HOMO, respectively, regardless of the structure type. On the other hand, the lowest unoccupied molecular orbitals (LUMO's) of DNA of both types are formed by the orbitals of Na and P O4, though the LUMO's of B-Poly (dA) *Poly (dT) and B-Poly (dG) *Poly (dG) are formed by thymine's and cytosine's LUMO when the DNA-DNA distance is more than 3 nm. The minimum energy gap between the valence edge and the empty state of Na and PO4 is 0.9 eV in A-Poly (dG) *Poly (dC). The narrow bandwidth of the valence and conduction bands show that the conduction arises not from band transport but a hopping mechanism in the presence of doping.