Surface-modified cation exchange materials are obtained based on industrial MK-40 heterogeneous and MF-4SK homogeneous cation-exchange membranes by in situ oxidative polymerization of aniline under electrodialysis conditions. The conduction and diffusion characteristics of the initial and modified membranes in solutions of sulfuric acid and nickel sulfate are studied. It is shown that the modification of the membranes with polyaniline leads to a decrease in their electrical conductivity and diffusion permeability without sacrificing high selectivity. The diffusion permeability of the cation-exchange membranes is higher in solutions of nickel sulfate in comparison with solutions of sulfuric acid, while an inverse dependence is found for anion-exchange membranes. The competitive transport of sulfuric acid and nickel sulfate during electrodialysis separation and concentration of their mixture using initial commercial and modified cation-exchange membranes paired with an MA-41 anion-exchange membrane is studied. It is shown that applying a layer of polyaniline with positively charged groups onto one of the surfaces of MK-40 or MF-4SK cation-exchange membranes leads to a decrease in the transport of a doubly charged nickel cation both in the separation and concentration modes over the entire range of current densities. The highest repulsion effect is observed in the case of the use of homogeneous modified membranes, where the selective permeability coefficient P(H2SO4/NiSO4) increases from 0.7–1.7 up to 32.5–19.7 depending on the current density. It is found that the use of surface-modified with polyaniline cation-exchange membranes makes it possible to concentrate a solution containing 0.1 mol-equiv/L (4.9 g/L) H2SO4 and 0.1 mol-equiv/L (7.7 g/L) NiSO4 with simultaneous separation to sulfuric acid with a concentration of about 2.4 mol-equiv/L (120 g/L) and a solution of nickel sulfate. Here, the concentration of nickel sulfate in the concentrate does not exceed 0.13 mol-equiv/L (10 g/L).