Under the background of energy internet and low carbon, a decentralized low-carbon economic dispatch model of electricity-gas interconnected network in which demand side management(DSM) and carbon trading are taken into consideration is proposed. Firstly, according to the actual situation of the carbon trading market, a step-type carbon trading mechanism is established, and the low-carbon characteristics of power to gas(P2G) are used to obtain the incentive mechanism for P2G to participate in the carbon trading market. Secondly, according to the existing DSM mechanism and implementation mode, the DSM is considered on the load side to maximize the coordination of network's low carbon and economic performance. Then, according to the non-convexity of the built model, the second-order cone relaxation of the gas network flow is performed and the continuous gap programming iterative algorithm is used to check its relaxation gap. The gradual reduction of the simulation error of the gas flow ensures the strictness of relaxation. In order to meet the decentralized autonomy and information privacy of different decision making subjects, a decentralized optimization model is built on the above basis and a synchronous alternating direction multiplier method (S-ADMM) is introduced to perform and iteratively solve the continuous cone programming algorithm. Finally, the simulation results of the system under different scenarios are analyzed and compared with the running results under different scheduling strategies. The results show that, under the tiered carbon trading mechanism, although the total carbon trading cost has increased by 0.02%, the carbon emissions and operating costs have reduced by 4.53% and 3.74%, respectively.The participation of DSM in the proposed model can reduce carbon emissions and wind curtailment by 9.87% and 75.4%, respectively.Therefore, the low-carbon economy of the electricity-gas interconnection network can be effectively improved. © 2021, High Voltage Engineering Editorial Department of CEPRI. All right reserved.