In this paper, we propose a novel gas-fuelled hot water system based on combined power and heat pump cycles. The proposed system essentially integrates a premixed gas burner, an organic Rankine cycle (ORC) power plant, and an air source heat pump for supplying hot water. An ORC power plant generates mechanical power from the thermal energy produced from the combustion of natural gas in the burner. Subsequently, the generated power directly drives a vapour compression cycle heat pump. Cold tap water is heated by three heat exchangers in series to gradually increase its temperature. It is preheated in the condenser of the heat pump, then heated in the condenser of the ORC power plant, and finally further heated by the flue gas exiting from the burner in a post heater. The flue gas exiting the post heater will be mixed with ambient air to further extract its residual heat in the evaporator of the heat pump. A comprehensive numerical analysis has been presented in this paper, and the results show that the proposed system can achieve an overall fuel-to-heat efficiency up to 147% when the cold water is heated from 10 to 65 degrees C and the ambient air temperature is in the range of -5 to 5 degrees C. The research results demonstrated that the proposed technology has a great potential for domestic hot water applications.