In spite of wide variety of commercial ion-exchange membranes, their characteristics, in particular, electrical conductivity and counterion permselectivity, are unsatisfactory for some applications, such as electrolyte solution concentration. This study is aimed at obtaining an anion-exchange membrane (AEM) of high performance in concentrated solutions. An AEM is prepared with a polypyrrole (PPy)-based modification of a heterogeneous AEM with quaternary ammonium functional groups. Concentration dependences of the conductivity, diffusion permeability and Cl− transport number in NaCl solutions are measured and simulated using a new version of the microheterogeneous model. The model describes changes in membrane swelling with increasing concentration and the effect of these changes on the transport characteristics. It is assumed that PPy occupies macro- and mesopores of the host membrane where it replaces non-selective electroneutral solution. Increasing conductivity and selectivity are explained by the presence of positively charged PPy groups. It is found that the conductivity of a freshly prepared membrane reaches 20 mS/cm and the chloride transport number > 0.99 in 4 M NaCl. A choice of input parameters allows quantitative agreement between the experimental and simulation results. However, PPy has shown itself to be an unstable material. This article discusses what parameters a membrane can have to show such exceptional characteristics.