Miniature Joule-Thomson refrigerators have been widely used for rapid cooling of infrared detectors, optoelectronic device, and integrated circuits of micro electronics. The typical J-T refrigerator consists of the recuperative heat exchanger with the double helical tube and fin configuration, J-T nozzle, a mandrel, Dewar and a compressed gas storage bottle. In this study, to predict the thermodynamic behaviors of the refrigerator with a compressed gas storage bottle during the cool-down time, numerical study of transient characteristics for a J-T refrigerator was developed. A simplified transient one.dimensional model of the momentum and energy equations was simultaneously solved to consider the thermal interactions of the each component of the refrigerator. To account for effects of the thermal mass of the solid, the heat capacities of the tube, fins, mandrel and Dewar are considered. The results show the charged gas pressure of the gas storage bottle has significant effects on the performance of the J-T refrigerator. At the elevated gas pressure of the gas storage bottle, the large capacity of the compressed gas storage does not need to get the fast cool-down performance of the J-T refrigerator in the cool-down stage.