A new tri-gate normally-off GaN metal-insulator-semiconductor field effect transistor (MISFET) is presented in this paper. By using a three-dimensional gate structure with combination of a sub-micron gate recess, the new device achieves a very low off-state drain leakage current of 0.6 mu A/mm at a breakdown voltage of 565 V while maintains a low on-resistance of 2.1 m Omega.cm(2). The new device has an on/off current ratio of more than 8 orders of magnitude and a sub-threshold 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.