We have theoretically analyzed electron transport in a Si atom wire at a finite bias voltage using a first principles method. Electronic states and transport properties are calculated using the Lippmann-Schwinger equation using the Laue representation in the framework of the density functional theory. We analyzed the transport properties of the Si wires between the metallic electrodes, and elucidated the effects of metallic contacts on Si atom wire, the character of conduction channels, and the dependence on the bias voltage. The conduction channels are analyzed using eigen channel decompositions and then it is found that the three channels contributing to the transport are open in the bias window under the finite bias voltage. [DOI: 10.1380/ejssnt.2009.17]