In the context of low-carbon economy and Energy Internet, the integrated electric power and natural gas system (IEGS) is an effective carrier to achieve regional resource optimization configuration and new energy consumption. This paper proposes an IEGS optimal scheduling model that takes into account the synergy between power-to-gas and carbon capture. By introducing a carbon capture power plant-electric gas-to-gas system synergistic utilization framework, the captured high-concentration carbon dioxide (CO₂) is used as a raw material power-generating equipment, and it is proposed that the use of gas storage devices to solve the CO₂ capture and utilization time is not matching questions. Aiming at the strong non-convex nonlinearity of the model, the model is transformed into a mixed integer second-order cone programming model by piecewise linearization and second-order cone relaxation. Finally, the improved continuous cone optimization method is used to ensure the strictness of relaxation. The simulation results show that the proposed model reduces the carbon emission and the amount of abandoned wind, and realizes the low carbon economy operation of IEGS, and the proposed algorithm can effectively improve the efficiency of the solution.