Miniature Joule-Thomson refrigerators have been widely used for rapid cooling of infrared detectors, probes of cryosurgery, thermal cameras, and missile homing head and guidance systems, due to their special features of simple configuration, compact structure and rapid cool-down characteristics. The cool-down time, the temperature at the cold end, the running time and the gas consumption are the important indicators of the performance of the Joule-Thomson refrigerator. In this study, a simplified one-dimensional model of momentum and energy transport for the recuperative heat exchanger was adopted to predict the thermodynamic behaviors of the refrigerator. In the analysis, to consider the thermal interactions of the each component of the refrigerator, the momentum and energy equations for the high pressure gas, the low pressure gas, the tube, the Dewar, and the mandrel were simultaneously solved. The thermodynamic properties from the REFPROP were used to account the real gas effects of the gas. The results show the effects of the supply pressure of gas on the transient behaviors of the temperature at the cold end and the thermal performance of the recuperative heat exchanger.