In this work, the capture of carbon dioxide using a dense hollow fiber membrane was studied experimentally and theoretically. The factors affecting the flux and recovery of carbon dioxide were studied using a lab-scale system. Experiments were conducted using a mixture of methane and carbon dioxide to simulate natural gas. The effect of changing the CO2 concentration from 2 to 10 mol%, the feed pressure from 2.5 to 7.5 bar, and the feed temperature from 20 to 40 °C, was investigated. Depending on the solution diffusion mechanism, coupled with the Dual sorption model, a comprehensive model was implemented to predict the CO2 flux through the membrane, based on resistance in the series model. Subsequently, a 2D axisymmetric model of a multilayer HFM was proposed to simulate the axial and radial diffusion of carbon dioxide in a membrane. In the three domains of fiber, the CFD technique was used to solve the equations for the transfer of momentum and mass transfer by using the COMSOL 5.6. Modeling results were validated with 27 experiments, and there was a good agreement between the simulation results and the experimental data. The experimental results show the effect of operational factors, such as the fact that temperature was directly on both gas diffusivity and mass transfer coefficient. Meanwhile, the effect of pressure was exactly the opposite, and the concentration of CO2 had almost no effect on both the diffusivity and the mass transfer coefficient. In addition, the CO2 recovery changed from 9% at a pressure equal to 2.5 bar, temperature equal to 20 °C, and a concentration of CO2 equal to 2 mol%, to 30.3% at a pressure equal to 7.5 bar, temperature equal to 30 °C, and concentration of CO2 equal 10 mol%; these conditions are the optimal operating point. The results also manifested that the operational factors that directly affect the flux are pressure and CO2 concentration, while there was no clear effect of temperature. This modeling offers valuable data about the feasibility studies and economic evaluation of a gas separation unit operation as a helpful unit in the industry.