We study the electron transport properties of a finite-length atomic chain created on an insulating substrate. Discrete energy levels are formed due to the finite length, and they are expected to show some trace in the I-V characteristics that are not predicted by an infinite chain model. Practically, electrodes are necessary for an electrical measurement but they cause complications : energy level broadening in the chain, chain charging due to the work function difference, Coulomb interaction through an effective capacitance, and mode selection resistance. If certain conditions are satisfied, depending on whether the highest occupied level is fully or partially filled in the chain, there is, respectively, an offset voltage for the current onset corresponding to the discrete energy separation, or the current rises rapidly for an infinitesimal voltage with a finite differential conductance on the order of quantum unit of conductance.