The density function theory is used to study the density profiles and the transport properties of an ion-exchange membrane system submitted to an electric potential drop. As the ionic density increases, hard sphere interaction between ions becomes dominant and the ion size must be taken into account. The results show that the density distribution and the transport properties depend on the bulk electrolyte density. At equilibrium the charge inside the electric double layer (EDL) adjacent to the membrane decreases and the membrane electric potential increases as the bulk density increases. For high bulk density of unsymmetric electrolyte, secondary charge layers are observed inside the EDL. In the membrane the anion-density-to-bulk-density ratio increases when the bulk density increases from small to moderate values owing to the membrane potential increase. But it decreases abruptly at high bulk density values owing to the increase of the non-ideal electrostatic interaction. At a given electric potential drop, the current/voltage curves follow the variation of this ratio with respect to the bulk density at equilibrium. As the current density approaches the limiting one, the amplitude of the secondary charge layers decreases and the EDL thickness increases.