In this paper, a novel combined heat and power (CHP) system is proposed in which the waste heat from a supercritical CO2 recompression Brayton cycle (sCO2) is recovered by a LiBr-H2O absorption heat pump (AHP). Thermodynamic and exergoeconomic models are established on the basis of the mass, energy, and cost balance equations. The proposed sCO2/LiBr-H2O AHP system is examined and compared with a stand-alone sCO2 system, a sCO2/DH system (sCO2/direct heating system), and a sCO2/ammonia-water AHP system from the viewpoints of energy, exergy, and exergoeconomics. Parametric studies are performed to reveal the influences of decision variables on the performances of these systems, and the particle swarm optimization (PSO) algorithm is utilized to optimize the system performances. Results show that the sCO2/LiBr-H2O AHP system can obtain an improvement of 13.39% in exergy efficiency and a reduction of 8.66% in total product unit cost compared with the stand-alone sCO2 system. In addition, the sCO2/LiBr-H2O AHP system performs better than sCO2/DH system and sCO2/ammonia-water AHP system do, indicating that the LiBr-H2O AHP is a preferable bottoming cycle for heat production. The detailed parametric analysis, optimization, and comparison results may provide some references in the design and operation of sCO2/AHP system to save energy consumption and provide considerable economic benefits.