We present a new normally-off GaN transistor-the tri-gate normally-off GaN metal-insulator-semiconductor field-effect transistor (MISFET). Due to the excellent channel control of a new 3-D gate structure, a breakdown voltage of 565 V has been achieved at a drain leakage current of 0.6 mu A/mm and V-gs = 0. The new device has an on/off current ratio of more than eight orders of magnitude and a subthreshold slope of 86 +/- 9 mV/decade. The threshold voltage of the new device is 0.80 +/- 0.06 V with a maximum drain current of 530 mA/mm. These results confirm the great potential of the tri-gate normally-off GaN-on-Si MISFETs for the next generation of power electronics.