Infrared spectroscopic ellipsometry from 9.5 to 12.5μm is used to study the nominally undoped GaN on sapphire. The parameters of the lattice vibration oscillators and the plasma are obtained by fitting with the experimental data. Then the anisotropic refractive index is calculated. Further-more, the carrier concentration and the electron mobility from the plasma frequency and the damping constant are derived. The result is compared with that of the Hall measurement.