Ultraviolet (UV) photodetectors are key devices required in the industrial, military, space, environmental, and biological fields. The Schottky barrier (SB)-MOSFET, with its high hole and electron barrier, and given its extremely low dark current, has broad development prospects in the optoelectronics field. We analyze the effects of trap states on the output characteristics of an inversion mode n-channel GaN SB-MOSFET using TCAD simulations. At the oxide/GaN interface below the gate, it was demonstrated that shallow donor-like traps were responsible for degrading the subthreshold swing (SS) and off-state current density (Ioff), while deep donor-like traps below the Fermi energy level were insignificant. In addition, shallow acceptor-like traps shifted the threshold voltage (Vt) positively and deteriorated the SS and on-state current density (Ion), while deep acceptor-like traps acted on a fixed charge. The output characteristics of the GaN SB-MOSFET were related to the resistive GaN path and the tunneling rate due to the traps at the metal (source, drain)/GaN interface. For the UV responses, the main mechanism for the negative Vt shift and the increases in the Ion and spectral responsivity was related to the photo-gating effect caused by light-generated holes trapped in the shallow trap states. These results will provide insights for UV detection technology and for a high-performance monolithic integration of the GaN SB-MOSFET.