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A reduction in brain disorders owing to traumatic brain injury (TBI) caused by head impacts in traffic accidents is needed. However, the details of the injury mechanism still remain unclear. In past analyses, brain parenchyma of a head finite element (FE) model has generally been modeled using simple isotropic viscoelastic materials. For further understanding of TBI mechanism, in this study we developed a new constitutive model that describes most of the mechanical properties in brain parenchyma such as anisotropy, strain rate dependency, and the characteristic features of the unloading process. Validation of the model was performed against several material test data from the literature with a simple one-element model. The model was also introduced into the human head FE model of THUMS v4.02 and validated against post-mortem human subject (PMHS) test data about brain displacements and intracranial pressures during head impacts.