We have studied the carrier concentration and the mobility in GaN expitaxial thin films deposited on sapphire substrate using infrared reflection spectroscopy. By theoretical calculation and fitting with the experimental IR reflection spectra for a series of Si-doped GaN epilayers and the sapphire substrate, we obtain the phonon vibrating parameters and plasmon frequency and damping constant in GaN. The carrier concentration and mobility have been deduced. The results show that the data for carrier concentration coincide with Hall measurement while the mobility is lower than Hall data by a factor of about 0.5. The variation of the LO phonon-plasmon coupling mode with doping level has been clearly observed. Raman measurement has been performed on the same series of samples, showing that the behavior of the LO phonon-plasmon coupling mode is similar to that in IR measurement.