We report on the power performance of GaN-on-Si metal-oxide-semiconductor high electron mobility transistors (MOSHEMTs) with a high-k ZrO2 gate dielectric formed by atomic layer deposition. As a result of the high-quality ZrO2 and ZrO2/AlGaN interface, the MOSHEMTs demonstrate an excellent ON/OFF current ratio of 5 x 10(10), a steep subthreshold slope of 66 mV/dec, a small hysteresis of similar to 0.05 V, and a high breakdown voltage of 1084 V at 1 mu A/mm. Effective suppression of current collapse with a dynamic-to-static ON-resistance ratio of 1.78 at a drain bias of 600 V is also achieved in the device. Benefiting from the highly uniform gate stack, large-area devices with a gate width of 20 mm were also demonstrated using the ZrO2 gate dielectric, exhibiting a maximum output current of 7.4 A, a low ON-resistance of 0.66 Omega, and a high breakdown voltage of 650 V at an OFF-state drain current of 1 mu A/mm.