In order to study the damage evolution and mechanical properties of solid propellants， uniaxial tensile and stress relaxation tests were performed on NEPE propellant. The resulting stress-strain curves and relaxation master modulus curves were obtained. A nonlinear viscoelastic constitutive model considering microscopic damage was developed under finite deformation. This model enables multiscale analysis of the mechanical response of propellants by incorporating the evolution of microvoids with various factors， including temperature， strain rate， confining pressure， and cyclic stress softening. The model was then implemented into ABAQUS with the parameters determined based on experimental data. Subsequently， the model was employed to predict the mechanical response of NEPE propellant under different loading conditions. The results demonstrate that the model accurately predicts the uniaxial tensile response of propellants under wide temperature ranges （223-333 K） and loading rates （1-200 mm·min^-1）. Moreover， the model exhibits reasonable predictability in cyclic loading， confining pressure tests， and biaxial tensile tests， thereby validating its effectiveness under complex stress conditions. Notably， the model necessitates only a small set of model parameters and can be easily programmed into commercial software， providing theoretical guidance for the multiscale analysis of the structural integrity of solid rocket motors.