Large-area graphene grown on Cu foil with chemical vapor deposition was transferred onto intentionally undoped GaN epilayer to form a graphene/GaN Schottky junction. Optical spectroscopic techniques including steady-state and time-resolved photoluminescence (PL) were employed to investigate the electron transfer between graphene and n-type GaN at different temperatures. By comparing the near-band-edge excitonic emissions before and after the graphene covering, some structures in the excitonic PL spectra are found to show interesting changes. In particular, a distinct "dip" structure is found to develop at the center of the free exciton emission peak as the temperature goes up. A mechanism that the first dissociation of some freely moveable excitons at the interface was followed by transfer of liberated electrons over the junction barrier is proposed to interpret the appearance and development of the "dip" structure. The formation and evolution process of this "dip" structure can be well resolved from the measured time-resolved PL spectra. First-principles simulations provide clear evidence of finite electron transfer at the interface between graphene and GaN.