Flow and acoustic fields of a transitional supersonic free jet with the moderate Reynolds number are investigated. Compressible Navier-Stokes equations are solved by a high-order compact scheme, and the effects of inflow shear layer characteristics are investigated. The Mach and Reynolds numbers are set to 2.1 and 70,000, respectively. Five different jets with different shear layer thicknesses and a jet with disturbances are computed, and the effects of the shear layer thickness and the disturbance are discussed. With decreasing the shear layer thickness or adding the disturbance, the transition position and the turbulence growth rate after the transition are significantly affected, and the turbulent fluctuation along the shear layer and the resulting Mach waves become smaller. The potential core length becomes shortest when the shear layer thickness is set to medium of the range we investigated, which might be explained by the position of turbulence transition and the growth rate after transition that are much affected by the inflow shear layer thickness.