The uniaxial compressive mechanical curves of nitrate ester plasticized polyether (NEPE) propellant under different temperatures and strain rates have been obtained with a universal testing machine and modified split Hopkinson pressure bar (SHPB). The experimental results show that the mechanical properties of NEPE propellant are both rate dependent and temperature dependent. With decreasing temperature or increasing strain rate, the modulus and rigidity obviously increase. Based on the previous models proposed by Yang and Pouriayevali, we propose a modified viscohyperelastic constitutive model which can describe the mechanical response over a large range of strain rates. Then we add a rate-dependent temperature item into the modified model to make a thermovisco-hyperelastic constitutive model. By comparing the experimental results with the model, we find that the thermovisco-hyperelastic constitutive model can correctly describe the uniaxial compressive mechanical properties of NEPE propellant at different temperatures and over a large range of strain rates from the static state to 4500 s−1.