Transcritical CO2 air-source heat pump has been widely applied for its high efficiency in producing domestic hot water. However, it preforms poorly for space heating specially in cold region, because of the high return water temperature and single-phase heat transfer in gas cooler. To resolve this issue, a modified integrated CO2 heat pump system is proposed, which can operate in heating-water combined mode and space heating mode with radiator followed by fan-coil unit in space heating circuit. To improve its thermal comfort and reduce economic cost simultaneously, multi-objective optimization for maximizing space-heating energy and minimizing total annual cost is conducted, based on a new optimizing model, considering two modes simultaneously as a whole and employing new concept of artificial neural network group. The best individual in Pareto front is selected, with 6109.2$/year cost and 5.87 × 108J heating energy. Corresponding optimal geometric parameters of components are obtained as follows, 0.378 m2 high-temperature gas cooler transfer area, 0.468 m2 low-temperature gas cooler heat transfer area, and 0.0015 m3/s compressor displacement. Moreover, effects of important factors (electric fee, water demand, and ambient temperature) on system performance are also investigated. This work presents a new optimizing model and reveals the excellent application potential of the new system.