The systematic thermodynamic optimization on the cooling performance of the hybrid cryocooler composed of multi-stage pulse tube and Joule-Thomson(JT) working at 1-2 K for cooling the Superconducting Nanowire Single Photon Detectors(SNSPD) is carried out. The structure design and working mechanism are described. An enthalpy flow model is proposed based on the thermodynamic cycle analysis, and a real fluid mass flow model for the temperature region below 3K is established. The two models are combined to analyze the hybrid cryocooler performance. The variations of the gross cooling capacity with the last stage precooling temperature and upstream pressure under ideal conditions are discussed and the proposed model is utilized to optimize the two variables by discrete parameter fitting method. For He-4 and He-3 working fluids, the optimal last stage precooling temperature of the multi-stage pulse tube is 11 K and 8 K, respectively. The results show that the hybrid cryocooler with He-4 as the working fluid can provide more than 85 mW cooling capacity at 2.2 K, and that with He-3 as the working fluid can provide 18.5 mW cooling capacity at 1.0 K. The performance of the hybrid cryocooler can meet the requirement of the practical applications of SNSPD.