Combined heat and power microgrids ( CHP-MG) can effectively utilize distributed energy resources． In orderto ensure the sustainable development of CHP-MG，it is necessary to take into account the economy of system operationand the low carbon and environmental protection． Therefore，the economic operation optimization and low-carbonsustainable development of CHP-MG are studied． Firstly，a two-stage demand response model is introduced to optimizethe electrical load on the demand side，and a transferable electric-thermal load model is constructed in the incentivedemand response to provide compensation costs for participating users． Secondly，the carbon ladder transaction costmodel and environmental cost model are constructed in the system to improve the environmental protection of the system．At the same time，the opportunity constrained programming model is used to deal with the uncertainty of wind，light andelectric-heat transfer loads． Finally，an example is given to verify the low carbon and economic performance of theproposed planning model．