Abstract: The visco-hyperelastic constitutive models of hydroxyl-terminated polybutadiene (HTPB) inhibitor were studied to describe the tensile mechanical properties accurately under finite deformation. Visco-hyperelastic constitutive model with rate related function and parallel constitutive model were built respectively, and the first model was multiplicatively combined by hyper-elastic model and rate related function, while the latter model was parallelly formed by hyper-elastic model and viscoelastic model containing damage factor. In order to fit the model parameters by the test data, the single-step relaxation test, multi-step relaxation test and uniaxial tensile test at various rates of HTPB inhibitor were undertaken. The results show that HTPB inhibitor is extremely sensitive to strain rate and has a great elongation, reflecting the obvious visco-hyperelasticity. Both of the models are able to predict the tensile mechanical properties of HTPB inhibitor in a large deformation range, meanwhile the model with rate related function can describe the mechanical properties more precisely, which is of great military significance.