We report a density functional non-equilibrium Green's function study of electrical transport in a single molecular conductor consisting of an ethane-dithiolate (C(2)H(4)S(2)) Molecular wire with two sulfur end groups bonded to the Au(1 1 1) electrodes. We show that the Current was increased by increasing the external voltage biases. The projected density of states (PDOS) and transmission coefficients T(E) under various external voltage biases are analyzed, and it suggests that the variation of the coupling between the molecule and the electrodes with external bias leads to the increase of the current. Furthermore, the investigation of the transport properties of the pentane-dithiolate (C(5)H(10)S(2)) molecular wire shows that the pentane-dithiolate molecular wire has a lower conductivity than the ethanedithiolate wire. (C) 2008 Elsevier B.V. All rights reserved.