A new device, known as a double-pass counterflow mass exchanger, is a circular tube divided by inserting a permeable barrier in parallel into two subchannels with sinusoidal wall fluxes, resulting in considerable improvement of the device performance in mass transfer compared with that in an open conduit. An analytical method is proposed to predict the concentration distribution and mass-transfer efficiency enhancement by setting a general solution form for the laminar double-pass counterflow concentric-tube mass exchangers with sinusoidal wall fluxes. Theoretical results show that a suitable adjustment of the permeable-barrier position can effectively enhance the mass transfer rate, leading to an improved device performance. The effects of the permeable-barrier location on the mass-transfer efficiency improvement and power consumption increment, as indicated from theoretical predictions, have also been delineated. One may follow the procedure described in the present paper and determine the economical feasibility for each particular application in operating double-pass devices.