A substantial increase in CO2/N-2 selectivity of the membrane under sub-ambient temperature conditions allows the design of CO2 capture processes in an energy-efficient and cost-effective manner. An innovative sub-ambient temperature membrane process is proposed in this study for the separation of CO2 from power plant flue gases, in which the high membrane selectivity is strategically utilized with the aid of a simple, external refrigeration cycle. In the new membrane process, a sweeping-integrated single membrane module integrated with a purification column is sufficient to achieve a high purity of 99.9% CO2 product with 90% CO2 recovery. Process optimization is utilized to determine cost-effective operating conditions and appropriate membrane configurations. The optimized sub-ambient temperature membrane process is shown to reduce the overall CO2 capture cost by 13% as well reducing the parasitic load by 16%, compared to a conventional multi-stage membrane process operated at ambient temperature conditions. The sensitivities of CO2 capture cost and energy with respect to key design variables such as pressure ratio, membrane performance (i.e. CO2 permeance and CO2/N-2 selectivity) and CO2 recovery are investigated to provide conceptual insights and design guidelines for developing efficient membrane processes for the capture of CO2.