The gas-liquid membrane contactor generally used as a nonselective gas absorption enhancement device is innovatively proposed as a condenser for heat recovery in liquid-absorbent-based carbon capture. The membrane condenser is used as a heat exchanger to recover the latent heat of the exiting vapor from the desorber, and it can help achieve significant energy savings when proper membranes with high heat-transfer coefficients are used. Theoretical thermodynamic analysis of mass and heat transfer in the membrane condensation system shows that heat recovery increases dramatically as inlet gas temperature rises and outlet gas temperature falls. The optimal split mass flow rate is determined by the inlet gas temperature and the overall heat-transfer coefficient in the condensation system. The required membrane area is also strongly dependent on the overall heat-transfer coefficient, particularly at higher inlet gas temperatures. Mass transfer across the membrane has an insignificant effect on heat transfer and heat recovery, suggesting that membrane wetting may not be an issue when a membrane condenser is used for heat recovery. Our analysis provides important insights into the energy recovery performance of the membrane condensation system as well as selection of operational parameters, such as split mass flow rate and membrane area, thickness, and thermal conductivity.