<p>In deep mining, retained rock with different degrees of initial damage may demonstrate significant rheological behaviors under high geostress. Traditional linear models fail to describe the non-linear accelerated creep properties of rocks and cannot characterize the influence of initial damage on creep properties. Considering this, creep tests were conducted on sandstone with different degrees of initial damage. In addition, a time-dependent damage model of rocks considering the effect of initial damage was established in conjunction with the improved Burgers model, Cowper–Symonds (CS) model, and theory of damage mechanics. The results indicate that creep stress affects the creep strain, and it determines the extent of the influence of initial damage on the creep strain in sandstone. The initial damage significantly influences the accelerated creep stage, and the creep failure stress linearly reduces and the time-dependent creep deformation time shortens with the rising degree of initial damage. The influence of initial damage on creep failure of samples is weakened with increasing confining pressure. The proposed time-dependent damage model of rocks considering the effect of initial damage overcomes the deficiency of traditional linear models in characterizing influences of accelerated creep and initial damage on creep properties. Based on the differential form of the time-dependent damage model, the secondary development of the time-dependent damage model is realized through the user-defined window of ANSYS/LS-DYNA, and the validity and correctness of the model are verified based on the experimental results and numerical examples. The research results provide theoretical guidance and reference for the study of creep mechanical properties and creep damage models, and also provide an important tool for the long-term stability prediction of caverns in practical engineering, which has significant engineering value and application potential.</p>