Abstract: Short fiber reinforced EPDM inhibitor film is a new type composite material, which has been applied in solid rocket motor winding and coating. Based on viscoelastic theory and fiber reinforced continuum mechanics theory, a transversely isotropic visco-hyperelastic constitutive model is proposed to describe strain rate dependent mechanical behaviors under vibration, impact and other loading conditions. The strain energy function is decomposed into hyperelastic strain energy and viscous strain energy, in which hyperelastic strain energy includes two parts: representing the strain energy from isotropic rubber matrix and anisotropic fiber tensile deformation. A macro-phenomenological model is proposed to characterize the viscous response from rubber matrix and fibers. Then, select the function form of each strain energy. After a series of mathematical transformation, substitution and superposition, the final form of stress and strain is determined. Moreover, the specific steps to obtain model parameters are defined. Finally, the predicted and experimental results are compared and analyzed, which indicates high accuracy of the proposed model. Studies show that it can effectively predict their nonlinear and strain rate dependent mechanical behaviors in the fiber direction from 0° to 45° at low strain rate. It is concluded that the proposed model is easy to realize finite element development, which has reference value for the structural integrity analysis of solid rocket motor.