It is known that ammonium has a higher permeability through anion-exchange and bipolar membranes compared to K+ cation that has the same mobility in water. However, the mechanism of this high permeability is not clear enough. We develop a mathematical model based of the Nernst-Planck and Poisson equations for diffusion of ammonium chloride through an anion-exchange membrane; proton exchange reactions between ammonium, water and ammonia are taken into account. It is assumed that ammonium, chloride and OH− ions can only pass through membrane hydrophilic pores, while ammonia can also dissolve in membrane matrix fragments not containing water and diffuse through these fragments. It is found that due to the Donnan exclusion of H+ ions as coions, the pH in the membrane internal solution increases when approaching the membrane side facing distilled water. Consequently, there is a change in the principal nitrogen-atom carrier in the membrane: in the part close to the side facing the feed NH4Cl solution (pH<8.8), it is the NH4+ cation, and in the part close to distilled water, NH3 molecules. The concentration of NH4+ reaches almost zero at a point close to the middle of the membrane cross-section, which approximately halves the effective thickness of the diffusion layer for the transport of this ion. When NH3 takes over the nitrogen transport, it only needs to pass through the other half of the membrane. Leaving the membrane, it captures an H+ ion from water, and the released OH− goes towards the membrane side facing the feed solution to meet the NH4+ ions. The comparison of the simulation with experiment shows a satisfactory agreement.