Gallium nitride (GaN) vertical Schottky barrier diodes (SBDs) with a SiNx field plate (FP) structure on low-dislocation-density GaN substrates have been designed and fabricated. We have successfully achieved the SBD breakdown voltage (Vb) of 680V with the FP structure, in contrast to that of 400V without the FP structure. There was no difference in the forward current-voltage characteristics with a specific on-resistance (Ron) of 1.1mcm2. The figure of merit V2b/Ron of the SBD with the FP structure was 420MWcm-2. The FP structure and the high quality drift layers grown on the GaN substrates with low dislocation densities have greatly contributed to the obtained results.