In order to describe the strain softening behavior and time-dependent characteristics of rock, an elasto- viscoplastic constitutive model is proposed considering the influence of time-dependent strain softening behavior. The new model was based on the sub-loading surface theory of over-consolidated soil and adopted the Hashiguchi' s sub-loading yield surface as a referenced yield surface. Besides, a relative overstress relation is used to obtain the dynamic loading surface at any strain rate based on the referenced yield surface. Two material parameters, c0 and m', which are related to the rate sensitivity, were added into the new model, and they can be determined by triaxial compression tests with different strain rates. The expansion index κand compression index λin the original model were replaced by elastic modulus E0 and deformation modulus Ed respectively, combining the characteristics of rock. A dynamic equilibrium condition, using the current stress, viscoplastic strain and viscoplastic strain rate as state variables, was adopted as a convergence criterion. After that, this model has been implemented into ABAQUS with the Newton-Raphson iteration. Simulations on the rate sensitivity triaxial tests of rock were conducted to verify the proposed model. The results show that the predicted results of model are in good agreement with experimental data. Meanwhile, material parameters are easy to understand and measure with clear physical meaning. Therefore, the proposed model can be used in the finite element calculation of complex boundary value problems.