With the growing concern for the environment, sustainable development centred on a low-carbon economy has become a unifying pursuit for the energy industry. Integrated energy systems (IES) that combine multiple energy sources such as electricity, heat and gas are essential to facilitate the consumption of renewable energy and the reduction of carbon emission. In this paper, gas turbine (GT), carbon capture and storage (CCS) and power-to-gas (P2G) device are introduced to construct a new carbon capture coupling device model, GT-CCS-P2G (GCCP), which is applied to the integrated electrical and gas system (IEGS). Multi-agent soft actor critic (MASAC) applies historical trajectory representations, parameter spatial techniques and deep densification frameworks to reinforcement learning for reducing the detrimental effects of time-series data on the decisional procedure. The energy scheduling problem of IEGS is redefined as a Markov game, which is addressed by adopting a low carbon economic control framework based on MASAC with minimum operating cost and minimum carbon emission as the optimization objectives. To validate the rationality and effectiveness of the proposed low-carbon economy scheduling model of IEGS based on MASAC, this paper simulates and analyses in integrated PJM-5 node system and seven nodes natural gas system.