Fractional calculus is a powerful mathematical tool for solving mechanical modeling problems. It is used to simulate soils between ideal solids and fluids. Using Riemann-Liouville's fractional calculus operator and theory, fractional order viscous element, nonlinear viscous element and viscoplastic body are connected in series to establish a fractional nonlinear creep damage model, which is used to simulate the nonlinear gradient process of rock creep under different water content conditions. The constitutive equation of the model is constructed. The parameters of creep damage model are identified based on the principle of least squares. The results show that the correlation between theoretical model and experimental data is more than 0.98, which can simulate the creep characteristics of rock well. The effect of model parameters on deformation is further explored, so that the effectiveness of model parameters can be analyzed and verified, and the applicability of the model in other complex stress environments is increased. The research results can provide theoretical basis for stability analysis and disaster prevention of soft rock slopes.