Traumatic brain injury (TBI) is one of the most important causes of death and disability. The objective of this study is to develop new head injury criteria which can predict the greatest principal strain and shear stress in the brain considering the impact directions and magnitudes. So, 150 head impact simulations were performed for 3 magnitudes and 50 directions of impact using head finite element model (FEM). Simulations were performed in order to assess the strain and shear stress created in the brain tissues due to different impact directions and magnitudes. Next, new head injury criteria were developed through performing statistical analysis. The simulation results showed that TBI risks in the sagittal and frontal planes were higher than those with impacts in transverse plane. Furthermore, new brain injury indices were developed to predict maximum principal strain and shear stress in the brain, which had correlation coefficients of 0.85 and 0.89 with head FEM responses, respectively. However, finding of present research showed the effects of impact directions on TBI risks. They also demonstrate that impact magnitude, direction, and duration should be used to develop a brain injury index.