A simple non-steady state mathematical model is proposed for the process of purification of an amino acid solution from mineral salts by the method of neutralization dialysis (ND), carried out in a circulating hydrodynamic mode. The model takes into account the characteristics of membranes (thickness, exchange capacity and electric conductivity) and solution (concentration and components nature) as well as the solution flow rate in dialyzer compartments. In contrast to the known models, the new model considers a local change in the ion concentration in membranes and the adjacent diffusion layers. In addition, the model takes into consideration the ability of the amino acid to enter the protonation/deprotonation reactions. A comparison of the results of simulations with experimental data allows us to conclude that the model adequately describes the ND of a strong electrolyte (NaCl) and amino acid (phenylalanine) mixture solutions in the case where the diffusion ability of amino acids in membranes is much less, than mineral salts. An example shows the application of the model to predict the fluxes of salt ions through ion exchange membranes as well as pH of the desalination solution at a higher than in experiments flow rate of solutions in ND dialyzer compartments.