By means of classic element combination modeling ideas

making fractional calculus soft-matter element and spring element in series and combining a visco-plastic body of power function

a new nonlinear viscoelasto-plastic rheological model with four elements is put forward. The constitutive equation and creep equation of the model are given and the creep curves in different stress conditions are obtained. It can be found that nonlinear gradual change process of steady creep phase and creep speed rate of accelerated creep stage of rock can be effectively simulated by adjusting creep parameters. In lower stress level

the model can describe the initial creep and steady creep of rocks. Moreover

if the stress level exceeds the long-term strength of rocks

the model can reflect the accelerated creep characteristics. The fitted results show that the nonlinear rheological model which contains soft-matter element and visco-plastic body of power function can effectively describe the creep properties of rocks and reduce the number of components and parameters of combination model.