Classical Nishihara model is difficultly to describe the nonlinear acceleration rheological properties of rocks. According to Riemann-Liouville fractional calculus theory, by replacing a Newton dashpot and viscoplastic dashpot in classical Nishihara model with fractional dashpot and nonlinear viscoplastic body(NVPB) model, a modified Nishihara model is proposed and a three-dimensional constitutive equation is deduced in the case of constant stress creep state. The rheological stage decomposition- particle swarm optimization(PSO)-simulated annealing intelligent algorithms is used for data inversion on existing experimental data. The results show that the model can effectively reflect the three-stage creep characteristics of rock. Through sensitivity analysis, it is found that the nonlinear gradual process and acceleration stage of rock are controlled by order of fractional derivatives and rheological index respectively. Furthermore, it is pointed out that the classical Nishihara model is a special case of the modified Nishihara model.