In order to decrease start-up time of a miniature Joule-Thomson cooler for IR detector, a Joule-Thomson cooler with precooler was applied. The refrigerant's temperature would be lower before throttling when Joule-Thomson cooler was precooled by precooler, and its temperature would be easier to reach IR detector's working temperature after throttling. Precooling would shorten start-up time of the Joule-Thomson cooler. Comparing the working theory of a single stage Joule-Thomson cooler and a Joule-Thomson cooler with precooler, the reason why a Joule-Thomson cooler with precooler starts up more quickly than a single stage one was illuminated. It will be better when a Joule-Thomson cooler and its precooler applies different refrigerants in the future study.