A novel type of ion-selective membranes, which combine the advantages of ceramic nanofibrous media with good electrical conductivity, is proposed. The membranes are produced from Nafen alumina nanofibers (diameter around 10 nm) by filtration of nanofiber suspension through a porous support followed by drying and sintering. Electrical conductivity is achieved by depositing a thin carbon layer on the nanofibers by CVD. Raman spectroscopy and TEM are used to confirm the carbon structure formation. The average pore size determined by low temperature nitrogen adsorption experiments lies in the range 15-30 nm. Measurements of membrane potential show that the carbon coated membranes acquire high ionic selectivity (transference numbers 0.94 for anion and 0.06 for cation in aqueous KCl). The fixed membrane charge is determined by fitting the experimental data to Teorell-Meyer-Sievers and Space-charge models.