Abstract: The viscoelastic and viscoplastic deformations of geo-materials are time-dependent energy dissipation behaviors. Within the framework of Rice irreversible internal state variable thermodynamics, two sets of internal state variables are introduced to describe structural rearrangement within solids during viscoelastic and viscoplastic deformation processes, respectively. The specific complementary energy function and the kinetic functons of internal state variables are presented, and the viscoelastic-viscoplastic constitutive equations are derived. The proposed viscoelastic constitutive equation has universality and can contain constitutive equations from classical viscoelastic models, such as the Kelvin-Voigt model and Poynting-Thomson model. The opinion that the linearity relationship between thermodynamic force and stress is the essential reason that the component model is linear is presented. The hardening effect of viscoplastic deformation can also be described accurately by the viscoplastic constitutive equation. A uniaxial creep test of an analogue material used to model geo-materials is conducted by loading and unloading paths. This method can separate viscoelastic and viscopalstic deformations in creep process. Then parameter identification is conducted through test data. Comparison between test data and theoretical curves indicates that the proposed constitutive equation can describe the creep behavior accurately, and can be a fundamental basis for forecasting and evaluating the long-term stability and analyzing the reinforcement of geo-material projects.