This study proposes the application of a precooler to the cascade mixed refrigerant Joule–Thomson (CMR J–T) cycle, herein referred to as the precooled CMR J–T (PCMR J–T) system. The purpose of the precooler is to utilize the temperature gradient characteristics within the two-phase region exhibited by the non-azeotropic mixed refrigerant. The precooler reduces the temperature of the high-temperature gas exiting the compressor by using cooling water from the condenser, thereby decreasing the capacity requirements of the high-temperature cycle (HTC). The working fluid comprises a nonflammable mixed refrigerant (R218, R23, R14, and Ar), and simulations were conducted by varying the HTC evaporation temperature and cooling water temperature for energy and exergy analysis. Under the analysis conditions, the capacity of each component in the HTC can be reduced by over 45%, leading to a maximum increase of 21.6% in the system’s coefficient of performance. Furthermore, the exergy destruction in the PCMR J–T system decreases along with the reduction in component capacity, with the most significant reduction occurring at the HTC expansion valve. The exergy efficiency of the system increases by up to 47.4%.