This study proposes three hybrid Schottky-ohmic gate structures for normally-off p-GaN gate AlGaN/GaN HEMTs. One has a Schottky-gate cover on the ohmic-gate and has part of the area contact to the p-GaN surface at the left and right sides of ohmic-gate (Structure A). The two others only have the Schottky-gate contact to the p-GaN surface at the left side (Structure B) or right side (Structure C) of the ohmic-gate. Different gate metal designs change the hole injection from p-GaN to GaN channel and show various gate leakages. The optimized contact length of Schottky-gate can suppress on-state gate leakage current over two orders of magnitude compared to conventional ohmic p-GaN gate HEMT. The improved on-state maximum drain current is over 60 mA mm-1 compared to Schottky p-GaN gate HEMT. Optimal performance in Structure B with Schottky-gate contact length ranges from 0.8 to 1.8 µm in a 2 µm gate geometry.