Quasi-vertical GaN barrier Schottky diodes have attracted much attention due to their low cost and high current transfer capability. The main problem lies 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 companying with other mechanisms are considered. Based on the established composite device models, the reverse leakage current is simulated which fits the recent experimental reports well. With the assistance of the proposed models, several field plate structures are discussed and simulated to get a quasi-vertical GaN barrier Schottky diode with high breakdown voltage. The major leakage mechanisms are also analyzed according to the linear dependence of leakage current, temperature and electric field in various reverse voltages. High BFOM up to 73.81MW/cm2 is achieved by adopting the proposed stepped field plate structure.