Abstract: Aiming at the problems of insufficient exploitation of the low-carbon dispatch potential for integrated energy systems (IES) and under-responsibility of carbon emission on the user side from the perspective of carbon flow, a low-carbon economic dispatch strategy for IES based on Stackelberg game considering adaptive stepped carbon potential-carbon price and dual response of supply and demand is proposed. First, an adaptive stepped carbon potential-carbon price model is designed. The IES carbon emission flow model based on the standardized matrix model of the energy hub is constructed to obtain the carbon potential of each energy load node on the user side and then complete the division of the carbon price interval under the carbon potential grading. Secondly, taking into account the flexible adjustment and response mechanism of the source and load sides, establish a low-carbon economic dispatch model of IES with user-side participation based on the Stackelberg game, the upper-level IES operator guides the lower-level user aggregator's decarbonized energy use through developing dynamically changing load nodes carbon potential-carbon price. Finally, the improved rime optimization algorithm (IRIME) is proposed to take advantage of its unique step-by-step search strategy that fits with the iterative process of the Stackelberg game and improve the design of weight coefficients and selection strategy to achieve high-precision and fast solution of the Stackelberg game model. The simulation results show that the proposed adaptive stepped carbon potential-carbon price model improves the carbon potential sensing ability of the user side, which can further reduce carbon emission by 4.76% compared with the stepped carbon emission fixed carbon price model, combined with the dual-response mechanism of supply and demand, it can improve IES operator revenue by 1.13% and reduce the user aggregator cost by 0.81%; IRIME enhanced the fastness of model solving while improving the equilibrium of inter-subjective game outcomes; and the proposed dispatch strategy realizes the flow transfer of the responsibility of carbon emission and the synergistic low-carbon economic operations between the two subjects.