We have investigated the characteristics of Au Schottky contacts to ZnO:N layers grown on (0001) GaN/Al2O3 substrates by plasma-assisted molecular-beam epitaxy. It is found that the Schottky characteristics are dependent on the growth temperature and polar direction of ZnO:N layers. The Schottky barrier height for the Au contact to a ZnO:N layer (300°C, Zn-polar) is estimated to be 0.66 and 0.69 eV by current-voltage measurements and capacitance-voltage measurements, respectively. It is found that the Schottky barrier height is proportional to the resistivity and incorporated N concentration of ZnO:N layers. Consequently, we believe that the low growth temperature and Zn-polar direction are favored for N incorporation in the growth of ZnO:N layers, which contributes to the increased resistivity in ZnO:N layers and results in good Schottky characteristics.