By HDR (hot dry rock) fracturing the deep buried geothermal energy can be efficiently extracted from the established EGS (enhanced geothermal system). While the fracture initiation and propagation is subjected to the interaction of cryogenic induced thermal stress and liquid pressure. Based on the mesodamage mechanics, elastic thermodynamics and Biot seepage mechanics, a mesoscopic thermo-hydromechanical-damage coupling model (THM-damage) is proposed to analyze the fracturing stimulation in HDR Firstly, the mathematical model and numerical implementation method is validated by high temperature granite fracturing experiments. Secondly, the action mechanism of thermal stress in hydraulic fracturing of HDR is discussed. Thirdly, the evolution of multiple physical fields during the initiation and propagation of HDR fracturing is researched. Finally, the effects of various parameters on HDR fracturing process are also studied. The results indicate that when the rock temperature exceeds 200 degrees C the fracture network can be formed by hydraulic fracturing, which extends along the direction perpendicular to the minimum in-situ stress. Increasing rock temperature can reduce fracture initiation pressure and rock failure pressure. The heat transfer coefficient between fracturing fluid and rock and the rock Young's modulus have influence on the fracture morphology during HDR fracturing under thermal stress. (C) 2019 Elsevier Ltd. All rights reserved.