In order to effectively describe the acceleration stage of rock creep and consider the compacting closure effect of rock fissures, a fractured plastic element is added to the model based on the fractional calculus theory. Then, a nonlinear creep model with five elements is established by introducing a variable section dashpot and a plastic element into a nonlinear visco-plastic body in parallel. The creep constitutive equation of this model is deduced, and the creep parameters are determined by fitting the data of rock creep test. The results show that the model can well describe three stages of rock creep, and it is reasonable and feasible.