We investigate the system-size dependence as well as the temperature dependence of the conductance in 1D electron systems, paying particular attention to the effect of Umklapp scattering. By taking into account the renormalization of the external potential due to electron-electron interaction, the correction to the conductance, 2e(2)/h, due to Umklapp scattering is estimated perturbatively. The Tomonaga-Luttinger liquid parameter appears in the conductance via the system-size and temperature dependence.