The supersonic mixing flow field of a Helium jet in cross-stream air is numerically simulated in the present study by solving the two-dimensional Reynolds-Averaged Navier-Stokes equations. Turbulence contribution is obtained from the Realizable k-ε and the SST k-ω model. Each model is incorporated separately with four different turbulent Schmidt numbers, i.e., 0.50, 0.35, 0.25, and 0.20. The focus of this paper is to guide the selection of a suitable turbulence model with an appropriate turbulent Schmidt number for these types of complex mixing simulations. The results show that both of the models can predict the general flow behavior while exhibiting their advantages. A better agreement with the experimental data is obtained when the turbulent Schmidt number is gradually decreased. However, examining the critical characteristics like upstream flow separation, bow shock prediction, and mass concentration of Helium the SST k-ω model with turbulent Schmidt number 0.20 can be considered for the reasonable estimation of the supersonic mixing flow field.