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Long-term strength (LTS) of rock materials is important for the long-term stability analysis and the failure prediction of structures in rock engineering. Numerous studies have been carried out on the LTS for various kinds of rock; however, the effects of initial damage on the LTS and creep failure time of rock have not been conducted. In the present study, the creep experiment with controllable initial damage state of rock was designed. Then, the LTS of rock specimens with different initial damage was determined by four methods (i.e., the isochronous stress-strain curve method, the steady creep discriminated method, the volumetric strain inflexion point determined method, and the intersection of the steady creep rate method). The results show that, with the increase in the initial damage, the LTS of rock decreases and the relationship between the initial damage and the LTS of rock can be described as a linear function. Finally, an evaluation method for predicting the creep failure time of rock under a single stress level was proposed. In addition, the creep failure time of rock with different initial damage under different creep stress levels was obtained by the method. The results indicate that both the initial damage and the creep stress levels have a great influence on creep failure time, i.e., greater initial damage or creep stress leads to a shorter period for rock failure. Thus, for analyzing the long-term stability of rock mass structure, not only the influence of in situ stress but also the initial damage state of the surrounding rock should be considered.