Off-state and vertical breakdown characteristics of AlGaN/AlN/GaN high-electron-mobility transistors (HEMTs) on high-resistivity (HR)-Si substrate were investigated and analysed. Three-terminal off-state breakdown (BVgd) was measured as a function of gate–drain spacing (Lgd). The saturation of BVgd with Lgd is because of increased gate leakage current. HEMTs with Lgd = 6 µm exhibited a specific on-resistance RDS[ON] of 0.45 mΩ cm2. The figure of merit (FOM = BVgd2/RDS[ON]) is as high as 2.0 × 108 V2 Ω–1 cm–2, the highest among the reported values for GaN HEMTs on Si substrate. A vertical breakdown of ∼1000 V was observed on 1.2 µm thick buffer GaN/AlN grown on Si substrate. The occurrence of high breakdown voltage is due to the high quality of GaN/AlN buffer layers on Si substrate with reduced threading dislocations which has been confirmed by transmission electron microscopy (TEM). This indicates that the AlGaN/AlN/GaN HEMT with 1.2 µm thick GaN/AlN buffer on Si substrate is promising candidate for high-power and high-speed switching device applications.