Streaming potential is one of the numerous electrokinetic phenomena created when an electrolyte flows along a charged surface. In membranes, applying the charged cylindrical pore model, streaming potential can be used to estimate, e.g., the pore size and the charge density of such pores. In this study, we are extending streaming potential experiments to ion-exchange membranes (IEMs) and trying to verify the existing models with the measurements. According to the Donnan equilibrium between an electrolyte solution and an IEM, the solution concentration should not affect the streaming potential if the membrane charge is even moderately low. Yet, the streaming potential varied substantially with the solution concentration, as in the case of nearly neutral porous membranes. In addition, the existing theory does not include the membrane thickness, but we found that thinner membranes showed larger streaming potentials. These dilemmas are discussed in this paper.