To extend the discretized virtual internal bond (DVIB) to viscoelastic materials, a viscous bond is introduced into the original DVIB, paralleling to the original hyperelastic bond. Through the coupled hyperelastic and viscous bonds, the micro viscosity mechanism can be accounted. The preliminary researches on the numerical simulation of the rock viscoelasticity are conducted by this method. It suggests that this method can represent the typical three-stage-feature of creep, the elastic delay, rate-dependency of rock strength and creep fracturing process. The further simulation suggests that the viscosity has significant impact on the dynamic fracture initiation, propagation and branching. It delays the fracture growth and weakens the fracture branching. A new and feasible approach to viscoelasticity simulation is presented in this paper.