Quasi-vertical GaN barrier Schottky diodes have attracted much attention due to their low cost and high current transfer capability. The main problem is that the reverse characteristics of the devices may not be well estimated, which affects the design of the diodes. In this paper, the defects of GaN materials and the leakage related tunneling mechanisms accompanied with other mechanisms are considered. Based on the established composite device models, the reverse leakage current is simulated which is well consistent with the recent experimental result. With the assistance of the proposed models, several field plate structures are discussed and simulated to obtain a quasi-vertical GaN barrier Schottky diode with high breakdown voltage. The major leakage mechanisms are also analyzed according to the relation among leakage current, temperature and electric field at various reverse voltages. High BFOM up to 73.81 MW/cm² is achieved by adopting the proposed stepped field plate structure.