To achieve lower temperatures is a subject of recent research and development activities in the field of pulse tube cryocoolers. To reach a temperature of 20K, multi-staging is necessary in Stirling-type pulse tube cryocoolers. In the present work, Sage software is used to design a three-stage gas-coupled as well as thermal-coupled pulse tube cryocooler. A single-stage and a two-stage pulse tube cryocoolers are developed, tested and are coupled by a thermal link to build up a three-stage thermal-coupled pulse tube cryocooler. The lowest temperature of 19.61K is obtained with a cooling capacity of 220mW at 30K at the third stage operating at 17bar charge pressure and 68Hz frequency. The phase-shifting mechanism used is a double inlet valve at the third stage while the inertance tube is used for the other stages.