Low natural gas prices are contributing to rapid growth in natural gas combined cycle (NGCC) power production in the United States. CO2 capture from the exhaust gas of these plants is complicated by the relatively low CO2 concentration in this flue gas (3%-4%). A membrane process using incoming combustion air as a sweep stream in a selective exhaust gas recycle configuration can be used to preconcentrate CO2 from 496 to 15%-20% with almost no energy input. Depending on the process configuration, the selective recycle membrane design reduces the minimum energy of a CO2 capture step by up to 40%. An all-membrane design using a capture step in series with a selective recycle membrane can capture 90% of CO2 from an NGCC power plant using less energy and at a lower cost than the base-case amine process analyzed by the U.S. Department of Energy. The current state-of-the-art membranes for use in this process have a CO2 permeance of 2200 gpu and a CO2/N-2 selectivity of 50. Higher CO2 permeance will improve the economics and reduce the footprint of a membrane CO2 capture system, while higher CO2/N-2 selectivity is of less benefit, because the process is limited by the affordable pressure ratio.