Comprehensive knowledge of strain rate-dependent viscoelastic properties of bony materials is necessary to understand the mechanisms of bone fracture under impact loading conditions (e.g., falls, traffic accidents, and military environments). Although the mechanical properties of bones have been studied for several decades, the high strain rate data and corresponding material parameters of the rate-dependent constitutive models are still limited. In this study, split Hopkinson pressure bar technique was used to test bovine cortical bones, to obtain the rate-dependent stress–strain curves in two directions (along and perpendicular to the bone fibers). A constitutive relationship comprising two terms was then applied to identify the material constants with strain rate effect and viscoelastic properties. In this model, the linear elasticity was combined with nonlinear viscoelasticity components to describe the overall nonlinear strain rate dependence. The presented data give strong experimental evidence and basis for further development of numerical biomechanical models to simulate human cortical bone fracture.