Traumatic Brain Injury (TBI) occurs when a mechanical insult produces damage to the brain and disrupts its normal function. Numerical head models are often used as tools to analyze TBIs and to measure injury based on mechanical parameters. However, the reliability of such models depends on the incorporation of an appropriate level of structural detail and accurate representation of the material behavior. Since recent studies have shown that several brain regions are characterized by a marked anisotropy, constitutive equations should account for the orientation-dependence within the brain. Nevertheless, in most of the current models brain tissue is considered as completely isotropic. To study the influence of the anisotropy on the mechanical response of the brain, a head model that incorporates the orientation of neural fibers is used and compared with a fully isotropic model. A simulation of a concussive impact based on a sport accident illustrates that significantly lowered strains in the axonal direction as well as increased maximum principal strains are detected for anisotropic regions of the brain. Thus, the orientation-dependence strongly affects the response of the brain tissue. When anisotropy of the whole brain is taken into account, deformation spreads out and white matter is particularly affected. The introduction of local axonal orientations and fiber distribution into the material model is crucial to reliably address the strains occurring during an impact and should be considered in numerical head models for potentially more accurate predictions of brain injury.