The itinerancy of π electrons included in DNA molecules is related to their structures and configurations. The variation of the itinerant electrons will affect the band structure of this kind of soft material to some extent. In the frame work of the tight binding model, we calculated the band structure and the electronic density of states of a DNA chain. It was found that the band gap at the Fermi level depends sensitively upon the number of the itinerant electrons. The conductance of the DNA molecule in different orders of duplex pairs with possible combinations was discussed.