The predicting equations for the mass-transfer rate and mass-transfer efficiency in a concentric circular membrane extractor module under concurrent- and countercurrent-flow with various barrier locations were derived theoretically by calculating the mass balance on each subchannel. The analytical solution was obtained by using the separation variable and eigen-function expansion in power series. The mass-transfer efficiency enhancement in this study is represented graphically with the volumetric flow rate and permeable-barrier location as parameters. The theoretical predictions show that the improvements in the extraction rate, extraction efficiency, and mass-transfer efficiency can be achieved by setting the barrier location moving away from the κ = 0.5. The influences of the barrier location, aqueous phase flow rate, and the concentrations of Cu2+ on the mass-transfer efficiency enhancement are also discussed.