Aeroacoustic fields of a supersonic free jet at the Mach and Reynolds numbers of 2.1 and 70 000, respectively, of the transitional conditions are computationally investigated by large-eddy simulations. The supersonic transitional jets of different shear layer thicknesses without disturbances and those of the fixed shear layer thickness with disturbances are computationally investigated, and the effects of the shear layer thickness and the disturbance are discussed. The position of the transition and the turbulence intensity in the vicinity of the transition are clearly affected by those parameters. The turbulent fluctuation along the shear layer and the resulting intensity of the generated Mach waves are substantially attenuated by decreasing the shear layer thickness or adding the disturbance. A 5 dB increase in the sound pressure level is observed. This relatively lower increment in the sound pressure level compared with the 10-20 dB increase in the subsonic jet case is discussed as being due to the transition process promoted by the spiral mode in the supersonic jet case, unlike the axisymmetric case in the subsonic jet case. This point is confirmed by the linear stability analysis, the proper orthogonal decomposition analysis, and the visualization of vortex structures in the transition region.