Kerr-like nonlinearity n(2) (THz) induced via terahertz (THz) radiation and linear electro-optic (EO) effect is investigated in (110), (111) and (100) oriented ZnTe crystals using Z-scan technique with femtosecond laser pulses. We have proposed a model, taking into account the Kerr-like nonlinearity n(2) (THz), to describe well the experimental incident polarization dependence of the nonlinear refractive index n(2). It is found that for a (110) ZnTe crystal the nonlinear refractive index n(2) is dominated by the Kerr-like nonlinearity n(2) (THz), while n(2) in the (111) ZnTe crystal mainly comes from the combined contributions of the Kerr-like nonlinearity n(2) (THz) and conventional Kerr nonlinearity n(2) (Kerr). We also show strong two-photon absorption (TPA) anisotropy and crystal orientation dependence of TPA in ZnTe crystals.