Combined heat and power (CHP) plants are operating under more fluctuating working conditions due to the increasingly inconsistent demands for heat and power and integration of renewable energy. This paper proposes to use an electric heat pump (EHP) to decouple heat and power and save energy by recovering waste heat from the cooling water. The thermodynamic model of the CHP unit under dynamic working conditions is established, and the dynamic EHP model based on an efficiency factor is proposed. The heat-power decoupling and energy-saving potential with different heat and power outputs and the heat pump DH ratio (χHP) are analyzed for a CHP unit as a case study. Absorption heat pump (AHP) and EHP-based waste heat recovery systems are also compared. The results indicate that the heat-power decoupling potential is bigger when χHP and the heat demand are increasing. The energy-saving effect is clearer by increasing the coefficient of performance (COP), χHP, or both. AHP and EHP can help the system obtain a certain level of heat-power decoupling and energy-saving effects, but these effects of the AHP-based system are smaller than that of EHP, especially under the working conditions of high heat demand and low power demand. •A heat-power decoupling method with waste heat recovery using large HP is proposed.•Thermodynamic model for CHP unit in dynamic working conditions is developed.•Integration of HP-based waste heat recovery system can bring energy-saving benefits.•Heat-power decoupling and energy saving with EHP is better than that with AHP.•The energy saving effect is improved by increasing COP or heating ratio of HP.