The electrical characteristics of graphene Schottky contacts formed on undoped GaN semiconductors were investigated. Excellent rectifying behavior with a rectification ratio of ~10 7 at ±2 V and a low reverse leakage current of 1.0 × 10 -8 A/cm 2 at -5 V were observed. The Schottky barrier heights, as determined by the thermionic emission model, Richardson plots, and barrier inhomogeneity model, were 0.90, 0.72, and 1.24 ± 0.13 eV, respectively. Despite the predicted low barrier height of ~0.4 eV at the graphene-GaN interface, the formation of excellent rectifying characteristics with much larger barrier heights is attributed to the presence of a large number of surface states (1.2 × 10 13 states/cm 2 /eV) and the internal spontaneous polarization field of GaN, resulted in a significant upward surface band bending or a bare surface barrier height as high as of 2.9 eV. Using the S parameter of 0.48 (measured from the work function dependence of Schottky barrier height) and the mean barrier height of 1.24 eV, the work function of graphene in the Au/graphene/GaN stack could be approximately estimated to be as low as 3.5 eV. The obtained results indicate that graphene is a promising candidate for use as a Schottky rectifier in GaN semiconductors with n-type conductivity.