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Hydrogen energy plays a crucial role in meeting the “carbon peaking and carbon neutrality” goals, and the carbon capture technology is a vital technique for emission reduction in the energy industry. Blending hydrogen with natural gas to produce hydrogen-enriched compressed natural gas (HCNG) facilitates the transportation and utilization of hydrogen energy. At the same time, applying the carbon capture technology to retrofit thermal power units can effectively promote the large-scale consumption of renewable energy and reduce carbon emissions. For this purpose, a detailed model of hydrogen production equipment and fuel cells is established. Then, aimed at the problem of system carbon emissions, a carbon emission and output model of carbon capture thermal power units and a mathematical model of hydrogen doped cogeneration are established, and a stepped carbon trading mechanism is introduced to control carbon emissions. Based on this, an optimal scheduling model for hydrogen-enriched compressed natural gas integrated energy system is established with the goal of minimizing the sum of energy purchase cost, carbon emission cost, wind abandonment cost, and carbon sequestration cost, and taking into account the constraints such as hydrogen blending ratio and carbon capture in the pipeline network, which is solved by using the particle swarm optimization algorithm in conjunction with CPLEX. The analysis of the models built in different scenarios verifies the advantages of the proposed scheduling model in low-carbon economy.