Abstract: To describe the nonlinear characteristics of the stable creep stage of rock, the evolution equations of the damage variable with time in the attenuation and constant velocity creep phases were derived based on the damage law proposed by Kachanov. Then the relationship between effective stress and creep time, initial damage variable, and minimum damage variable was obtained using the Lemaitre strain equivalence principle. The effective stress was substituted for the Caucy stress in the generalized Kelvin creep model, and the generalized Kelvin creep model considering the initial damage was established. According to the triaxial compressive creep test data of sandy mudstone in Bojianghaizi Coal Mine, the generalized Kelvin creep damage model was identified. The identification results showed that the generalized Kelvin model considering the initial damage has a very good agreement between the theoretical curve and the experimental curve, and it is much better than the traditional generalized Kelvin model in describing the attenuation and steady stages.