To provide a control method for a freezing cycle and a freezing cycle using the method wherein it can effectively be operated by controlling the degree of supercooling when the operation is performed under subcritical conditions in a freezing cycle with carbon dioxide used as a refrigerant.

The degree of supercooling is set to be about 15°C when high pressure side refrigerant pressure is nearly at a critical point, and as the high pressure side refrigerant pressure is reduced from the neighbourhood of a supercritical point, the degree of the supercooling is gradually reduced. A freezing cycle for realizing such a control method includes a compressor, a heat radiator 3 for cooling a refrigerant pressure of which is raised, an expansion valve 5 for reducing the pressure of a refrigerant, an evaporator 6 for vaporizing a refrigerant, and detection means 10 for detecting pressure and refrigerant temperature upstream the expansion valve 5. When the refrigerant temperature upstream the expansion valve 5 is nearly at a critical point, the degree of supercooling is set to be about 15°C, and the expansion valve travel is controlled such that as the refrigerant pressure upstream the expansion valve 5 is reduced from the neighbourhood of the critical temperature, the degree of supercooling is gradually reduced along a control line.