Abstract: The study of rock constitutive behavior under the thermal-mechanical action is of guiding significance in rock engineering such as exploitation of deep resources, exploitation of geothermal resources and construction of deep-buried long and large underground structures. Based on the recent researches of rock damage deteriorating constitutive model, through strict mathematical deduction, a thermal-mechanical-damage constitutive model considering crack initiation strength is established by introducing three parameters, Weibull distribution, thermal damage and Drucker-Prager yield criterion, and residual strength correction coefficient. The expressions for its parameters are determined. Then the constitutive model is verified by the results of biotite granite triaxial compression tests under confining pressure of 25 MPa and different temperatures of 20℃, 60℃ and 130℃. The results show that the theoretical curves match up to the experimental ones, which can objectively reflect the relationship between stress and strain, and the residential strength during the rock deformation and failure process under TM condition. Furthermore, the model parameters have clear physical meaning. Finally, using the proposed constitutive model to analyze the mechanical response of the Swedish APSE tunnel excavation process by numerical analysis software FLAC, the modelling results can reflect the TM damage features of tunnels.