The numerical analysis of the supersonic jet is conducted using large eddy simulations (LES) with high order schemes and the grid of approximately 650 million points. A Mach number and a Reynolds number are set to be 2.0 and 9.0×105, respectively. At first, we confirm the azimuthal grid resolution. As a result, it seems that the flow field and the acoustic field near the jet flow are slightly affected by changing the grid resolution, while the sound pressure level at far-field converges sufficiently with the present grid number. The computational flow field shows good agreement as compared with the experimental data. Moreover, it is shown that the sound pressure level at far-field can be predicted within 4dB difference as compared to the experimental data. Next, the effect of the jet temperature of the supersonic jet on the acoustic waves is investigated. The temperature ratio of the chamber to ambient air is set to be 1.0, 2.7, and 4.0 for the cold, mid-hot and hot jets, respectively. Mach waves are radiated from the supersonic jet toward downstream. we confirmed that the shorter potential core length, the higher sound pressure level, the larger angle of Mach waves with increasing jet temperature.