  We study a finite quantum wire connected to external leads, and show that the
conductance of the system significantly depends upon the length of the quantum
wire and the position of the impurity in it. For a very long quantum wire and
the impurity far away from its two ends, the conductance has the same behavior
as that for an infinity quantum wire above some very little energy scale.
However, for a very short quantum wire, the conductance is independent of the
electron-electron interactions in it and closing to $e^{2}/(2\pi\hbar)$ in a
higher temperature range. While, in a lower temperature range, the conductance
shows the same property as that for an infinity quantum wire.
