The performance on mass transfer for a membrane gas absorption process was investigated theoretically and experimentally in the present study. Physical absorption of carbon dioxide by water was carried out and illustrated to validate the theoretical predictions. A two-dimensional mathematical formulation was developed in a hollow fiber gas–liquid membrane contactor with gas and liquid flow rates regulated independently. The resultant partial differential equations, as referred to conjugated Graetz problems, were solved analytically using the separated variable method associated with an orthogonal expansion technique. The absorption efficiency was studied with the absorbent flow rate, gas feed flow rate and CO2 concentration in the gas feed as parameters. Both good qualitative and quantitative agreements were found between the theoretical predictions and experimental results. The accuracy of the theoretical predictions for concurrent flow in hollow fiber gas–liquid membrane contactor is 5.18×10−2≤E≤7.21×10−2.