During the process of oil-gas drilling, the problems of wellbore instability, such as the shrinkage and the sloughing of borehole, usually happen because of rock creep. We first analyzed the three stages of rock creep based on the law of the conservation of energy and explained the reason why the traditional rock creep model cannot well describe the accelerating stage of rock creep. Then, we modified the Nishihara model and relevant constitutive equations by increasing a winding device. Some experimental results of several kinds of rocks forming different formations were used to validate the modified Nishihara model. The verification results indicate that this model can describe the creep characteristic of rock effectively. Especially the accelerating creep stage of rock can be simulated very well when the stress exceeds the long-term strength. This modified Nishihara model provides a theoretical foundation for revealing the objective law of the rock creep.