In order to characterize the mechanical response of double-base propellant， the viscoelastic properties and constitutive model of double base propellant were studied. Firstly， the viscoelastic properties of double-base propellant were investigated by tensile， compression and stress relaxation experiments with an observation of fracture surface. Then， a hyperelastic-viscoelastic model of double base propellant was established based on the Reduced Polynomial（N=5） model and Prony series. The parameters of the developed model were obtained by the experimental data. Finally， the hyperelastic-viscoelastic model of double base propellant was verified. The relatively error between the results of the simulation calculated by the hyperelastic model and the experiment for uniaxial tensile stress-strain is less than 5.01%. The relatively error between the results of simulation and experiment for stress relaxation is less than 6.49%. The developed hyperelastic-viscoelastic constitutive model of double-base propellant can well describe the mechanical properties of double base propellant， which provides a significant method for the research of mechanical properties of propellant.