In this study, a rate-dependent biphasic model will be introduced to account for phenomenological behavior of brain tissue. For this purpose, a poro-hyper viscoelastic constitutive model is developed. The tissue is treated as a fluid-saturated porous medium, modeled as biphasic matter constituting of a solid matrix and interstitial liquids fill the porous spaces. The interactions between the two phases are assumed to be governed by Darcy’s law. This suggested model is calibrated with the experimental results of the bovine brain tissue, tested under high deformation rates (10, 100, 1000 mm/sec). The model will successfully take care of the detailed mechanical responses for solid and fluid phases, and their contributions to morphological behavior of this biological tissue. The material parameters of the model have been examined to agree well (R2 ≥ 0.96, where R is the coefficient of determination) with various deformation rates. In addition to representing the complete mechanical response and deformation of the solid phase, this biphasic model demonstrates the flow and diffusion of the liquid through the tissue networks.