Rocks may exhibit time-dependent behaviors. Long-term strength criterion significantly dominates creep failure of rocks. Rocks contain many microcracks, which lead to degrade of long-term strength. In this paper, it is assumed that there exist three-dimensional penny-shaped microcracks in rocks. The mode II stress intensity factors at tips of three-dimensional penny-shaped microcracks in Burgers viscoelastic rock matrix is derived. A novel micromechanics-based three-dimensional long-term strength criterion is established to consider the effects of time and the intermediate principal stress on creep failure of rocks. By comparison with the previous experimental data, it is found that the novel micromechanics-based three-dimensional long-term strength criterion is in good agreement with the experimental data.