Rock creep exhibits significant nonlinear characteristics, which become particularly pronounced during the accelerating creep stage under high shear stress, primarily due to the continuous accumulation of internal damage. The Nishihara model fails to adequately describe this phenomenon. To better characterize the full-stage creep process, this study introduces a damage variable into the component model based on damage mechanics theory and Lemaitre's strain equivalence principle, taking into account the full-process damage evolution. First, based on damage mechanics theory and the strain equivalence principle, a composite creep model consisting of a damaged generalized Kelvin model and a triggered nonlinear damage acceleration element is constructed. Finally, the Levenberg–Marquardt nonlinear least squares method is applied to fit selected experimental data, verifying the rationality of the theoretical model. The results show that the proposed full-process damage creep model can effectively describe the entire rock creep process, with the correlation coefficient between the fitted curves and experimental data exceeding 0.95.