A process for recovery of CO2 from a post-combustion gas includes pre-concentrating a CO2 component of the post-combustion flue gas by passing the post-combustion gas through a CO2-selective membrane module to provide a CO2-enriched permeate stream and a CO2-lean reject stream. Next, in a CO2 absorber, both the CO2-enriched permeate stream and CO2 lean reject stream, fed to separate feed locations on the CO2 absorber, are contacted with a scrubbing solvent to absorb CO2 and provide a carbon-rich scrubbing solvent. Finally, absorbed CO2 is stripped from the carbon-rich scrubbing solvent by a two-stage CO2 stripping system. The CO2-selective membrane may be a high flux, low pressure drop, low CO2 selectivity membrane. The two stage stripping system includes a primary CO2 stripping column for stripping CO2 from the carbon-rich scrubbing solvent exiting the CO2 absorber, and a secondary CO2 stripping column for stripping CO2 from a carbon-lean scrubbing solvent exiting the primary CO2 stripping column. Apparatus for CO2 removal from post-combustion gases in a pulverized coal power plant incorporating the described processes are described.