Abstract: In order to reflect the whole creep deformation process of rock under the coupling thermal-mechanical action, the critical damage stress is derived on the basis of fracture mechanics principle and a new non-linear viscous component correlated to the critical damage stress is proposed to describe the rock creep deformation in the steady stage. The exponential damage variable, critical damage and its related non-linear viscous component are introduced into the rheological differential equation based on the raditional Nishihara creep model and Burgers mode. By using the superposition principle, the rheological constitutive relation of rock is derived under the uniaxial and triaxial compression conditions considering the effect of temperature. The coupling thermal-mechanical damage creep model is established for rock. Comparison is presented between the calculations of this damage creep model and test data of granite under the conditions of different temperatures and stresses. The results show that this damage creep model can well simulate the creep deformation characteristics of rock in the initial creep stage, the steady-state creep stage and the accelerating creep stage, which verifies the validity and rationality of the damage creep model developed in this paper. This model may provide an important theoretical basis for analyzing the long-term stability of rock engineering under the conditions of high temperature and stress.