Abstract: Based on the classical element model, the nonlinear element and the creep damage are introduced to solve the problem that the classical element model cannot describe the non-linear characteristics of rock during the whole compressive creep process. Firstly, the inaccuracies of these methods in the identification of model parameters, the establishment of equation for damage creep and the selection of yield conditions are analyzed. After that, an elastic body, a non-linear Kelvin body, a viscous body and a damage viscoplastic body are constructed based on the non-linear rheological theory and damage theory, and the four bodies are connected in series to establish a damage creep model which can simultaneously describe the instantaneous elastic strain, the non-linear viscoelastic strain, the viscous strain and the non-linear viscoplastic strain of rock. The one-dimensional and three-dimensional differential damage constitutive equations for rock under constant stress are derived, and the equation for damage creep is obtained according to the superposition principle. Considering the characteristics of creep curve, a simple and feasible identification method for model parameters is given. Finally, the applicability of the model is verified by comparing the creep test curve of sandstone under uniaxial and triaxial compressions with the theoretical curve and prediction curve. The results show that the proposed model fits well the test data. The viscoelastic-plastic damage creep model can accurately reflect the non-linear characteristics of creep curves in attenuation and steady stages and describe the accelerated creep characteristics of rocks in high stress state.