A double-pass parallel-plate mass exchanger under asymmetric wall concentrations is designed by inserting in parallel a permeable membrane to improve the device performance. A mathematical model was formulated theoretically for such double-pass forced-convection mass exchangers, as referred to conjugated Graetz problems. Linear superposition was introduced to analytical solutions of the resultant partial differential equations, which consists of an inhomogeneous solution with respect to the non-homogeneous boundary condition and a homogeneous solution is obtained with the use of an eigenfunction expansion in a power series. The analytical results show that the mass transfer efficiency of this double-pass parallel-plate mass exchanger is considerably enhanced as compared to that of a single-pass device by suitably adjusting the permeable-membrane position. Economic consideration in terms of the mass transfer efficiency and power consumption increment for double-pass operation is presented.