In order to accurately characterize the various stages of the rock creep curve, the viscous coefficient of the viscous pot element in the Kelvin model is defined as a time-dependent function and a damage viscoelastic body is constructed by considering the deterioration of creep parameters over time according to the creep damage theory. Then, the elastomers, nonlinear Kelvin body, viscous body and damage viscoelastic body are connected in series, and a nonlinear viscoelastic plastic damage creep model that can describe the entire process of rock creep is proposed. The one-dimensional and three-dimensional creep equations of the model under constant stress are reasonably derived. Finally, a parameter identification is performed based on relevant creep test data to verify the effectiveness of the damage creep model. A comparative analysis is conducted on the correlation between the theoretical model and experimental data, and the results show that the model can well describe the entire process of rock creep, with correlation coefficients above 0.92.