To study the creep characteristics of interbedded rock mass when considering the effect of time-dependent deformation. This paper proposes a non-constant viscoelastic plastic five-element model considering stress and strain thresholds. The model can simultaneously describe the instantaneous elastic strain, viscoelastic creep, linear viscoplastic creep and nonlinear viscoplastic creep (accelerated creep) of the rock, and derives its creep equation under the three-dimensional stress state. Based on the ABAQUS finite element software, the development of the UMAT subroutine was completed, and the applicability of the model was verified by comparing the indoor creep test of the rock with the numerical simulation results of the model. The results show that the results of the creep test are consistent with the results of the numerical calculations. The non-constant viscoelastic-plastic novelty model can not only accurately describe the decelerated creep and steady-state creep processes, but also can better describe the accelerated creep process of rocks. This verifies the applicability and effectiveness of the model.