The mathematical modeling formulation for predicting the carbon dioxide absorption by amine in a concentric circular membrane contactor with spiral wire channel under countercurrent-flow operations was developed theoretically and experimentally in the present study. The numerical method applied in modelling carbon dioxide absorption process in the system was the Runge–Kutta method with shooting method. The correlated equation of Sherwood number was investigated implementing with experimental data to predict the mass transfer coefficient for the carbon dioxide absorption by amine, and thus, the theoretical predictions of absorption efficiency enhancement were represented graphically and validated by the experimental results within acceptable accuracy. The new design of a concentric circular membrane contactor with spiral wire channel can effectively enhance the carbon dioxide absorption efficiency among various operating and design conditions. The absorption efficiency, average Sherwood number and concentration distributions were represented graphically with the absorbent flow rate, gas feed flow rate and inlet CO2 concentration as parameters. The influences of operating and design parameters in the new device on the absorption efficiency and total absorption rate are also discussed.