This study has demonstrated AlGaN/GaN metal-insulator-semiconductor high electron mobility transistors (MIS-HEMTs) on Si substrates with a SiNx/SiON composite gate dielectric. The threshold voltage shift in the devices was investigated. The MIS-HEMTs with the SiNx/SiON composite gate dielectric exhibited superior threshold voltage uniformity and small threshold voltage hysteresis than the reference device with SiNx only gate dielectric. The variation of the device threshold voltage was mainly related to trapping process by the interface states, as confirmed by band diagrams of MIS-HEMTs at different gate biases. Based on frequency-dependent capacitance measurements, interface state densities of the devices with the composite and single gate dielectrics were extracted, where the former showed much smaller interface state density. These results indicate that the SiNx/SiON composite gate dielectric can effectively improve the device performance of GaN-based MIS-HEMTs and contribute to the development of high-performance GaN electronic devices.