The invention discloses a gas cryogenic liquefying system. A heat exchange unit comprises a primary heat exchanger E1, a secondary heat exchanger E2 and a tertiary heat exchanger E3 which are in tandem connection in sequence, wherein the input end of the primary heat exchanger E1 is connected to a compression unit; the output end of the tertiary heat exchanger E3 is connected to the input end of an expansion liquefying unit; the output end of the expansion liquefying unit is connected to a gas-liquid separating unit; a refrigerant input end of the tertiary heat exchanger E3 is connected to the gas output end of the gas-liquid separating unit; a refrigerant output end of the tertiary heat exchanger E3 is connected to a first refrigerant input end of the primary heat exchanger E1; a first refrigerant output end of the primary heat exchanger E1 is connected to the compression unit; a refrigerant input end of the secondary heat exchanger E2 is connected to a finished product output end of the gas-liquid separating unit; or the output end of the primary heat exchanger E1 is connected to the refrigerant output end of the secondary heat exchanger E2 and the compression unit. According to the gas cryogenic liquefying system, the whole process is simpler and more practical, package is easily realized, energy consumption of a refrigerating machine is avoided, and pollution of a conventional refrigerant and the like is avoided.