The AlGaN/GaN Schottky barrier diodes (SBDs) working as high-power mixer and multiplier show great potential in millimeter wave (MMW) field owing to their high breakdown voltage. Nevertheless, its further application is severely limited by large reverse leakage current (Jr) since the two-dimensional electron gas (2DEG) channel is hard to be pinched off at low voltage. To address this limitation, a graded AlGaN/GaN heterostructure is introduced to extend the 2DEG channel into a quasi-three-dimensional electron slab. By comparing the fixed Al composition AlGaN/GaN SBD, Jr of the graded AlGaN/GaN SBD is significantly reduced due to the extension of channel carriers, confirming the effective Jr suppression effect of this structure. Furthermore, on this basis, a recessed anode structure is utilized to expect a smaller Jr. The results indicated that the graded AlGaN/GaN SBDs with air-bridge structure have achieved a pretty low Jr value (1.6 × 10−13 A at -15 V), and its cutoff frequency is as high as 60.6 GHz. It is expected that such SBDs with low Jr have significant advantages in future applications.