The fluidic thrust vector nozzles including the shock-induced thrust vector nozzles stand out from traditional mechanical thrust vector nozzles used in aeronautics and astronautics due to their simplicity and potential for higher efficiency. However, a significant challenge in the transition from theoretical studies to practical applications is the phenomenon of self-excited oscillation of the nozzle jet, particularly in ramjet and scramjet engines. This oscillation can notably impact the jet control stability, which is critical for the operational reliability, accuracy, and safety of these engines. To investigate the effects of self-excited oscillation of the jet in the three-dimensional rectangular shock-induced thrust vector nozzles, a large eddy simulation approach has been utilized to examine various nozzle pressure ratios and secondary pressure ratios. The simulation data are in good agreement with the experimental data of National Aeronautics and Space Administration Langley Research Center, lending credibility to the simulation results. The research sheds light on the formation and evolution of self-excited oscillation. It does so by examining the interactions between shock waves and boundary layers, as well as bubble dynamics, offering a comprehensive view of the oscillation mechanism in a three-dimensional context. The results demonstrate that the self-excited oscillation of jet mainly belongs to low-frequency oscillation. With the increase in nozzle pressure ratio, the self-excited oscillation of the jet is suppressed because the shock system is pushed out of the shock-induced thrust vector nozzle exit. The variation of secondary pressure ratio only affects the amplitude of jet self-excited oscillation and does not transform the motion pattern.