In order to verify the predictive ability of the method used in this paper about screeching jet, the numerical simulation was used for modeling in different mach number. The SAS - SST model was adopted to model the two-dimensional axisymmetric under-expanded supersonic jet turbulent field-flow. Spatial discretization was based on the Roe scheme, and the dual time step method was used in the time discretization, and the far field boundary was adopted the non-reflective boundary condition. The formation of the shock cell structure was simulated. The computed of the flow-field of schlieren figure and the different position of pressure and density values in the flow field were compared with the experiment data. Moreover, the wavelength, frequency and sound pressure level of the screech tone were investigated for the jet noise. All of the data were in good agreement with the experimental value, and the method could accurately capture the screech tone mode switch. In addition, when considering the far-flow conditions, the amplitude of screech noise decreased so that could be helpful to weaken the acoustic fatigue of the nearby mechanical structures. The results showed that the method could be used to study the prediction and mechanism of screech tone, which provided an important reference for the next step to analyze the high mach number screeching jet and the method of supression the screech noise. © 2019, Science Press. All right reserved.