A series of Si doped GaN thin films grown on sapphire substrate were measured by Raman spectroscopy. Both high-and low-frequency branches of the longitudinal-optical (LO) phonon and plasmon coupling modes (LPP modes) were resolved. With the increasing of doping level, the LPP mode shifts toward higher frequency. The two branches in each spectrum were independently lineshape-fitted based on scattering analysis, and plasmon frequency and damping constant were obtained, thus the free carrier concentration and mobility could be deduced. The carrier concentration derived from each branch of the single spectrum coincidences with each other, and it is also consistent with infrared (IR) reflection and Hall results. The mobility from the low branch fitting is in agreement with the IR values, and is about half values of the Hall mobility, which is close to the conduction drift mobility in the regime of ionized impurity scattering. The high branch mobility is even smaller, which implies some additional scattering effect.