We report a first-principles study of electrical transport in a single molecular conductor consisting of ethane-dithiol (C2H4S2) sandwiched between two Au (100) electrodes. We show that the current was increase with increasing the external voltage biases. The projected density of states (PDOS) and transmission coefficients under some 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. Therefore, we propose that the most origin of electron transport mechanism in molecular devices is caused by the characteristics of the molecule and the electrodes as well as their cooperation. Furthermore, the transport properties of the buthane-dithiol (C4H6S2) molecular wire are also investigated. The results show that the buthane-dithiol molecular wire has a lower conductivity than the ethane-dithiol ones at a given external biases thus; it is a better insulator device for the molecular electronics technology.