Temperature is an extremely important parameter for the material of the space-borne infrared detector. To cool an HgCdTe-infrared detector, a Stirling-type pulse-tube cryocooler (PTC) has been developed based on a great deal of numerical simulations, which are performed to investigate the thermodynamic behaviors of the PTC. The effects of different low temperatures are presented to analyze different energy flows, losses, phase shifts, and impedance matching of the PTC at a temperature range of 40–120 K, where woven wire screens are used. Finally, a high-efficiency coaxial PTC has been designed, built, and tested, operating around 60 K after a number of theoretical and experimental studies. The PTC can offer a no-load refrigeration temperature of 40 K with an input electric power of 150 W, and a cooling power of 4 W at 60 K is obtained with Carnot efficiency of 12%. In addition, a comparative study of simulation and experiment has been carried out, and some studies on reject temperatures have been presented for a thorough understanding of the PTC system.