We report the fabrication of AlGaN/GaN high electron mobility transistors (MIS-HEMTs) with a high breakdown voltage by employing a metal-insulator-semiconductor (MIS) gate structure using Si3N4 insulator. The Si3N4 films were deposited by plasma enhanced chemical vapor deposition (PECVD) as the surface passivation, interlayer films and the gate dielectric. In comparison with Schottky-gate HEMTs, the gate leakage currents of MIS-HEMTs exhibited three orders of magnitude reduction. With similar device structures, the off-state breakdown voltage of MIS-HEMTs was 1050 V with a specific on-resistance of 4.0 mΩ cm2, whereas the breakdown voltage and specific on-resistance of SG-HEMTs were 740 V and 4.4 mΩ cm2, respectively. In addition, the MIS-HEMTs exhibited little current slump in the pulsed measurements and possessed faster switch speed than Si MOSFET. We demonstrate that AlGaN/GaN MIS-HEMTs are promising not only for microwave applications but also for high power switching applications.