We numerically study the intrinsic localized vibrational modes in a diatomic chain with different masses and alteating force constants between nearest neighbors. This model simulates a row of atoms in the 〈111) direction of sphalerite-structure crystal. We found that the harmonic and quartic anharmonic terms in the nearest-neighbor interaction potential produce the intrinsic localized modes with frequencies above the optical branch or in the gap of the linear spectrum, the distribution pattes of atom amplitudes are asymmetry with a form of quasi-even-or quasi-odd-parity, and the inclusion of cubic term in the potential lowers the frequencies of the modes and introduces static displacements for the atoms.