A three-dimensional elastic–viscoplastic (3D EVP) model focusing on shear hardening is proposed to describe the time-dependent behaviors of sand. In developing this model, a one-dimensional elastic–viscoplastic (1D EVP) equation of deviatoric stress–strain–strain rate is first derived based on the analysis of stress relaxation tests on four different sands and the equivalent time method suggested by Yin and Graham. Subsequently, the 1D EVP equation is generalized into triaxial state by referring Lade-Duncan’s elastic–plastic theory and Perzyna’s overstress theory. The proposed 3D EVP model incorporates shear yield criterion, non-associated flow rule, and strain-hardening law, which makes it possible for the model to describe the rate effects and shear dilation characteristic. Finally, numerical solutions are obtained using the fourth-order Runge-Kutta method, and the model is calibrated and verified through several experiments. It is demonstrated that the new model is capable of predicting rheological behaviors of dilatant sand, especially the shear-induced volumetric responses.