In order to deal with the problem of low-carbon operation of power system, this paper takes the two-way coupled integrated electricity-gas system (IEGS) as the research object, introduces carbon capture technology and carbon trading mechanism, and studies the low-carbon economic dispatching problem of integrated electricity-gas system in carbon capture power plant. Firstly, the energy consumption characteristics of carbon capture are analyzed, and some CO2 is absorbed by electricity to gas. By comparing and analyzing the traditional carbon trading mechanism with the stepped carbon trading mechanism, it is proved that the stepped carbon trading mechanism is more conducive to the low-carbon operation of the system. Secondly, a low-carbon economic scheduling model of integrated electricity-gas system considering carbon capture cost and carbon transaction cost is established. Through linear transformation and improved second-order cone relaxation method, the non convex nonlinear model is transformed into a mixed integer convex optimization model. Finally, the simulation results on the modified IEEE 30-bus power system and Belgium 20-bus natural gas system show that the model established in this paper can effectively realize the low-carbon economic operation of system.