Numerous studies have shown that highly strainrate dependent behavior is present in the mechanical properties of Hydroxyl-terminated polybutadiene(HTPB)propellants, and many experts and scholars have attempted to develop constitutive models to describe such rate-dependent properties of propellants. From the linear viscoelastic model to the Zhu-Wang-Tang model, the strainrate dependent properties of viscoelastic materials have been described to some extent. But due to the highly nonlinear mechanical behavior exhibited in propellant materials, the nonlinear behavior of propellants at different strain rates is difficult to be captured in the above constitutive models which are all based on linear elasticity. Therefore, in this paper, a nonlinear viscoelastic constitutive model was proposed based on the parallel rheological framework, in which the hyperelastic and viscoelastic flow laws were em-bedded. Because of the excellent ability to capture the nonlinear behavior of the material, the parallel rheological framework was used to predict the mechanical response at six sets of experiments with different rates. Surprisingly, this constitutive structure model performed good prediction of the mechanical properties of the material by comparison between theoretical calculations and experimental data. The constitutive model was verified by finite element method with numerical simulation software, and the robustness of the constitutive model was checked by a new set of experimental data. A good foundation was established for the accurate description of the propellant constitutive model strain-rate dependent characteristics by the results of this paper, which could provide a new method for the rapid prediction and evaluation of the propellant mechanical response.