The rate of transport of ions through an annular ion-selective membrane having an elliptic cross section is analyzed. This is a generalization to a hollow-fiber type of device, and represents a wide class of membranes which are capable of providing a large (surface area/volume) ratio for ion transport. The Nernst-Plank equation governing the transport of ions is solved numerically. The results obtained reveal that, if the concentration of fixed charge is high, its current efficiency is insensitive to fixed charge distribution, and the local electroneutrality can be assumed. On the other hand, if the concentration of fixed charge is low, the distribution of fixed charge becomes significant, and assuming local electroneutrality can be inappropriate. In general, the higher the average concentration (or the greater the total amount) of tired charge of a membrane, the higher its current efficiency. We show that the results for planar and cylindrical membranes can be recovered from the present model.