The invention discloses a gas system capable of achieving repeated refrigerating and heating output. The gas system capable of achieving repeated refrigerating and heating output comprises a gas unit, a smoke waste heat acting unit, a first gradient heat pump unit, a second gradient heat pump unit and a smoke output pipeline. The gas unit is used for driving a compressor of the first gradient heat pump unit. One end of the smoke output pipeline communicates with a gas outlet of the gas unit. A gas inlet and a gas outlet are formed in the smoke waste heat acting unit. The other end of the gas output pipeline communicates with the gas inlet of the smoke waste heat acting unit. The two ends of the smoke delivery pipeline are connected with the gas unit and a first waste heat acting unit. The smoke waste heat acting unit is used for converting heat energy of smoke exhausted by the gas unit into kinetic energy and driving a compressor of the second gradient heat pump unit. According to the gas system capable of achieving repeated refrigerating and heating output, mechanical energy of the gas unit and heat energy of smoke can be fully used, and the energy utilization rate of gas is increased.