The invention provides a system with an extraction condensing unit changed into a back pressure unit on the basis of a spraying heat pump and an operation method of the system. The system is reasonable in structural design and efficient, and saves energy. The system comprises a high-pressure cylinder, a low-pressure cylinder, a boiler, an oxygen removing device, a water feeding pump, a high-pressure heater, a boiler water feeding pipeline, a main steam input pipeline, the spraying heat pump, a water supplementing heater, a cooling device, a control system, a first valve, a second valve, a third valve, a high-pressure heat supply steam pipeline, a low-pressure heat supply steam pipeline, a high-pressure drive steam pipeline, a water supplementing heater water input pipeline and a water supplementing heater water output pipeline. For heat users requiring high-pressure steam parameters, the spraying heat pump injects low-pressure heat supply steam with high-pressure drive steam, and the high-pressure heat supply steam pipeline supplies the high-pressure heat supply steam. When the requirement for temperature of the high-pressure heat supply steam needed by the heat users is not high,the water supplementing heater is additionally arranged in the high-pressure drive steam pipeline, and the boiler supplies water to cool and drive the high-pressure drive steam of the spraying heat pump.