Nitrate ester plasticized polyether (NEPE) solid propellant was widely used in carrier rocket and guided missiles, owing to its excellent mechanical properties, high specific impulse and good performance of low temperature storage. The material of NEPE suffered from thermal cycle, high pressure impulse and vibration during service life. Thus, the mechanical properties of NEPE had important implications for the safety of structure and service life. Experimental results indicated that the material presents significant time-dependence and nonlinear characteristics. In order to clarify the damage mechanism of NEPE solid propellant, the mesostructure evolution was investigated with the 3D in-situ observations by using synchrotron radiation computed tomography (SR-CT). The voids initiated at the interface between matrix and particles and propagated along the loading direction. With the increasing of loading, matrix breaking, particles breaking and debonded particles were observed in the near-surface regions. Furthermore, a visco-hyperelastic constitutive model coupling damage was proposed to describe the mechanical behavior of NEPE under finite deformation. The constitutive model provides a good simulation with experimental results, which is meaningful to the structure integrity assessment of NEPE solid propellant.