To overcome the shortcoming that the traditional component assembly model is difficult to describe the nonlinear characteristics of rock creep process, a new time-triggered nonlinear viscous component was proposed for series connection with the generalized Kelvin model. Then, the modulus attenuation equation of rock elasticity modulus during the rock creep process was introduced into the generalized Kelvin model to obtain a nonlinear creep model that can simulate the whole process of rock creep. Then, the one-dimensional and three-dimensional creep equations under different constant loads were derived. According to the general global optimization algorithm, parameter determination and model verification of the nonlinear creep model were performed by using the rock creep experiment curve of previous researches. The comparison between the theoretical calculation value of the model and the rock creep experiment curve shows that the nonlinear creep model is highly accurate and rational. It can better simulate the creep deformation of rock at different stress levels, and can provide certain reference value for carrying out similar researches in the future.