Single-crystal gallium oxide (Ga2O3) metal-oxide-semiconductor field-effect transistors were fabricated on a semi-insulating β-Ga2O3 (010) substrate. A Sn-doped n-Ga2O3 channel layer was grown by molecular-beam epitaxy. Si-ion implantation doping was performed to source and drain electrode regions for obtaining low-resistance ohmic contacts. An Al2O3 gate dielectric film formed by atomic layer deposition passivated the device surface and significantly reduced gate leakage. The device with a gate length of 2 μm showed effective gate modulation of the drain current with an extremely low off-state drain leakage of less than a few pA/mm, leading to a high drain current on/off ratio of over ten orders of magnitude. A three-terminal off-state breakdown voltage of 370 V was achieved. Stable transistor operation was sustained at temperatures up to 250 °C.