In this work, using a tight-binding Hamiltonian model, a generalized Green's function method and Lowdin's partitioning techniques, some of the significant properties of the conductance of, poly (dG) -poly (dC) DNA molecule in SWNT/DNA/SWNT structure are numerically investigated. In Fishb ne model, we consider DNA as a planar molecule which contains M cells and 3 further sites (one base pair site and two backbone sites) in each cell sandwiched between two semi-infinite single-walled carbon nanotubes (SWNT) as the nano-electrodes. Relying on Landauer formalism as the basis for investigating the conductance properties of this system, we focus on the studying of the electron transmission and the current-voltage characteristics of DNA in the foregoing structure. In addition, in the presence of the electric potential between DNA molecule ends, our results suggest that the increasing of the value of applied bias give rise to the large enhancement in the conductance of the system. We also find that, as the tube radius increases, the conductance of the system considerably increases.