In recent decades, the fluidic thrust vector control technique is one of the core strategies to redirect various aerospace vehicles, such as modern launch rockets, supersonic aircraft, and guided missiles. The fundamental theory of the shock vector control is that the gas is injected into the supersonic part of a conventional convergent–divergent nozzle from the transverse to cause interactions between the shock waves and boundary layers. Then, the deflection of the primary jet can be easily realized by the induced oblique shock waves. It was evident that the shock vector control is a very simple, low weight, low cost, and quick vectoring response technique to gain high thrust vectoring performance. In the present work, computational fluid dynamics studies were performed at different control parameters in a three-dimensional rectangular supersonic nozzle with the slot injector. For the validation of the numerical methodology, computational results were compared with experimental data referred to the NASA Langley Research Center. The static pressure distributions along the upper and lower nozzle surfaces in the symmetry plane were matched with the test data excellently. Numerical simulations were based on the well-assessed shear stress transport k–ω turbulence model. Second-order accuracy was selected to reveal more details of the flow-field as much as possible. Lots of factors were investigated, such as the momentum flux ratio, length-to-width ratio, injection location, and injection angle. The performance variations for different affecting factors were illustrated and some constructive conclusions were obtained to provide the reference for further investigations in fluidic thrust vector control field.