The application of the recycle-effect concept to a double-pass parallel-plate mass exchanger under asymmetric uniform wall concentrations is proposed to enhance device performance. An analytical analysis of the Sherwood number and mass-transfer efficiency improvement is developed, and the theoretical predictions are represented graphically and compared with those in single-pass devices without inserting a permeable membrane. A considerable mass-transfer efficiency improvement is obtained by employing such a recyclic design with a suitable adjustment of the permeable-membrane location and recycle ratio, instead of using the single-pass device without external recycle. The results show that the recyclic double-pass operation can effectively improve the mass transfer efficiency, especially as the device is operated in the larger mass-transfer Graetz number.