Implicit large-eddy simulations (LES) are performed in this work to study the flow-field and acoustic characteristics of a highly-heated rectangular supersonic jet. The focus is on the nozzle pressure ratio(NPR) effects. Three NPRs are investigated including 3.0, 3.67, and 4.0, which correspond to the nozzle over-expansion, perfect-expansion, and under-expansion conditions respectively. The current hot jet has a nozzle temperature ratio (NTR) of 7.0, corresponding to a total temperature of around 2100K. The rectangular nozzle has an aspect ratio of 2.0 and has been extensively tested at the Universityof Cincinnati. An in-house CFD code with an artificial dissipation mechanism is used to perform the large-scale implicit LES computations. By studying the pressure contours, density gradients and dilatation, it is found that the three-dimensional jet shock/expansion wave structure changes signifi-cantly when the jet NPR increases from an over-expanded to under-expanded condition. The length of the laminar shear layer right outside the nozzle is extended to the downstream before transitioning to be turbulent. The distance between the nozzle lip and the first shock cell is doubled while the total number of shock cells keeps the same, which results in a longer jet potential core. The increase of nozzle NPR also provides about an 11% increase in jet velocity and a 25% increase in shear layer convection Mach number, which leads to a stronger Mach wave radiation noise component in the acoustic fields. Pressure spectra in the near field reveal that screech only exists in the over-expansion case and the broadband shock-associated noise is enhanced in the perfect and under expansion cases.The far-field acoustics at 40Deq is characterized by about 4 dB increase of the overall sound pressure level in the Mach wave radiation direction and about 2 – 3 dB increase in all other directions. The far-field pressure spectra also confirm that the screech noise component vanishes when the nozzle NPR is increased to perfect- and under-expanded conditions.