Abstract: In view of the distinct mechanical responses exhibited by solid propellants across a wide range of strain rates, the three-dimensional fractional-order Maxwell constitutive model and its difference iterative scheme were derived by using the Grünwald-Letnikov definition of the fractional-order operator. The ability of the fractional-order viscoelastic model to characterize the constitutive relationship of NEPE propellants under a wide range of strain rates was systematically investigated. Based on the Split Hopkinson pressure bar tests and high-speed tensile experimental data of NEPE propellants, the parameters of the fractional Maxwell constitutive model were identified using a genetic algorithm, and the fractional Maxwell constitutive model was verified using the test data at strain rates of 3 500 s⁻¹, 4 100 s⁻¹ and 4 600 s⁻¹. The results demonstrate that this constitutive model exhibits a strong rate dependence. For the high, medium and low strain rates, the viscoelastic mechanical behavior under multiple strain rates can be well characterized by a set of parameters respectively. The relative errors between the full-duration experimental values and the analytical solutions are basically less than 20%, while those between the analytical solutions and finite element numerical solutions are less than 2%. This validates the feasibility and accuracy of the three-dimensional fractional-order Maxwell model in describing the mechanical behaviors of NEPE propellants over a wide range of strain rates.