Energy efficiency and greenhouse gas emissions mitigation are important topics in modern energy systems research. In this study, power-to-gas (P2G), carbon capture, supercritical CO2 (S–CO2) cycle systems are integrated into a carbon cycle system, and the role of the carbon cycle system in the electricity-heat integrated energy system (IES) is explored. The carbon capture system collects the CO2 produced by coal-fired and gas-fired units, which can be recycled in two ways. One is sent to P2G device to react with the hydrogen produced by electrolysis of water. The other part is sent to the S–CO2 unit as the supplementary working fluid. In addition, the waste heat of the gas-fired unit and the heat released in P2G are collected as additional heat supply. This work focuses on the optimal dispatch in an IES with carbon cycle system connection. The optimization results show that with the orderly regulation of the carbon cycle subsystem, the wind power and photovoltaics' curtailment rates can be reduced by 3.1% and 10.8%, respectively. And the system's carbon emissions are reduced by 89.5%. Besides, IES's energy and exergy efficiencies increase by 1% and 0.9% after applying the carbon cycle system.