Cryocoolers working in the liquid hydrogen temperature are important for applications such as cryo-pump, superconductor cooling and cryogenic electronics. This paper analyzes and compares the 20K gas-coupled two-stage Stirling type pulse tube cryocooler with and without pre-cooling. The pre-cooling uses some of the cooling power generated by the first stage cold head to pre-cool the middle of the second stage pulse tube. Given the same input acoustic power, the simulation results show that the cooling capacity of the second stage increase from 0.64 W to 2 W@20 K while the first stage available cooling capacity decrease from 5.84 W to 3 W@77 K when the pre-cooling is used. Meanwhile, the cryocooler relative Carnot Efficiency in terms of acoustic power increases from 10.3% to 14.6%.