The integrated community energy system (ICES) can realize the economic and environmental protection. As the critical equipment for ICES, energy router (ER) can realize the flexible transformation of different energy carriers. However, the efficiencies of the energy conversion devices in ER are usually assumed to be constant for the sake of simplicity, which may result in out-of-order operation schemes and redundant costs of ICES. In addition, the forms of multiple energy coupling of ICES are complex, and the conventional methods are difficult to coordinate the multiple energy demands. This article proposes a demand side management (DSM) method for ICES. Firstly, a dynamic ER model is built to determine the energy conversion efficiency with the variation in load rate. The energy hub model provides a mathematical representation of ER, considering energy demand and the availability of different energy sources. Then, the DR considering renewable energy output is proposed, where a real-time price strategy is established and determined by the power of load demand and generation of renewable energy. Finally, a multi-objective operation optimization strategy based on low-carbon and the economy is established. The model involves the device constraint in the process of energy production and energy transmission. The simulation results of the proposed model under different scenarios are compared. The results show that the model effectively improves the economic benefits of ICES and reduces carbon emissions, and alleviates the pressure on the energy supply.