The absence of cold moving parts in pulse tube cryocoolers has allowed it to has advantages of low vibration, high reliability, and low cost, which can meet requirements of many high-temperature superconducting applications. However, Stirling type pulse tube cryocoolers working around 20 K are still not commerally aviable due to low efficiency and low power density. With Comprehensive consideration of higher specific power of whole system and performance in relative lower working temperature of 20K, this paper proposes a thermally coupled two stage co-axial pulse tube cryocooler to pursue several watts cooling power around 20K.At the first stage, an ultrahigh frequency operation of 100 Hz is utilized to precoo the second stage for seeking a higher power density. At the second stage, a relative lower frequency of around 30Hz is used for improving system efficiency. Firstly, a quasi-one-dimensional numeric model based on the thermoacoustic theory is used to optimize the operating and structure parameters and some simulation results are briefly introduced. The influences of different phase shifters such as doule-inlet and room temperat ... mehrure displacers are also also investigated numerically. Then, in the experiments, typically a lowest no-load temperature of 13 K has been obtained and the cooling power at 20K was 2 W with an input electric power of 500 W, which mean an efficiency of 5.6% of Carnot. The influences of different operating and structure parameters such as frequency, mean pressure and precooling temperature were also investigated numerically and experimentally.