[en] Current-voltage (I-V) characteristics have been measured to clarify the charge transport mechanism in the charge order state of a two dimensional organic conductor α-(BEDT-TTF)₂I₃. At low temperatures, we find strong non-linear I-V characteristics that follow the power law approximately. The non-linear I-V characteristics are attributed to the electric-filed-assisted unbinding of excited pairs of an electron and a hole that attract each other due to two-dimensional long-range Coulomb interaction. We also report a larger anisotropy in the dielectric constant, which shows the highly two-dimensional nature of the Coulomb interaction in the BEDT-TTF layers.