Natural rock contained a large number of microcracks generated and accumulated in the long-term geological activity. In early loading stages or under a low stress level, rock would experience a fracture compression phase, in which rock showed out nonlinear instantaneous plastic deformation. Without considering rock instantaneous plastic deformation by fracture compression, the normal rock creep model reflected lower instantaneous deformation value than the real. Therefore, it is necessary to consider effect of initial damage on rock creep in process of constructing rock creep constitutive model. Considering different degrees of initial damage existing in the natural rock and new damage caused by crack extension under loading in the process of rock creep, the creep properties of rock with initial damage in different stress levels is overall described. With the increase of stress, rock creep would experience steady creep with instantaneous elastic deformation, steady creep with instantaneous elastoplastic deformation and accelerated creep. Based on the relationship between stress and normal deformation of the unclosed structural plane, concluded by BANDIS S C and BARTON N R through many tests, a mechanical component of fracture rock plastic deformation body is put forward to describe instantaneous plastic deformation in rock creep process. Considering the initial damage having effect on accelerated creep, an initial damage factor is introduced to Kachanov creep damage variable evolution equation, a damage variable evolution equation of the rock with initial damage is built. Furthermore, a creep damage body component is put forward to simulate accelerated creep of rock. The fracture rock plastic deformation body component and the creep damage body component are series connected to the generalized Kelvin model which can describe instantaneous elastic deformation and viscoelastic deformation of rock, to form a whole creep process constitutive model which could reflect instantaneous elastoplastic deformation, steady creep and accelerated creep of the rock with initial damage. The method of model parameters determination through a small amount of tests is put forward. At different stress levels, the theoretical curves can coincide with the creep test curves. The new rock creep model can simulate nonlinear increase of instantaneous deformation by stress level. Compared to accuracy of the accelerated creep simulation only by traditional Kachanov creep damage variable evolution equation, the accuracy of the new model has been improved after introducing the initial damage factor.