Most rocks exhibit time-dependent deformation and failure. Two main mechanisms are generally considered, the progressive growth of cracks and viscoelastic and/or viscoplastic deformation. In this study, cracking process is described by a viscous phase-field method which is coupled with a viscoplastic model. The evolution of crack field is controlled by both elastic and viscoplastic tensile volumetric and deviatoric strains. The threshold of viscoplastic deformation is weakened by the growth of cracks. The efficiency of the proposed model is first assessed by comparing numerical predictions with experimental data in triaxial compression and creep tests. Then, the proposed model is applied to modeling time-dependent deformation and failure process of a high slope section in the left bank of Jinping-I hydropower station in China. Numerical predictions are compared with field measurements.