In the engine combustion test using the hypersonic wind tunnel facility, high temperature, high pressure, and high velocity flow is generated by combustion heating upstream of the nozzle. However, in this process, the turbulence of the flow and the contamination by the combustion gas occur unavoidably. Therefore, it is a concern that the different situation is observed between the ground test and actual flight because of these unavoidable factors. In this study, we focus on the mixing process of the injected fuel and the free-stream and aim to numerically evaluate the influence of the free-stream turbulence on the jet mixing. The LES calculation with free-stream turbulence is performed by the inflow boundary condition applying the velocity, temperature, and pressure fluctuations based on the Random Flow Generation (RFG) method, strong Reynolds analogy (SRA), and an isentropic process. The input parameter for RFG can control the generated free-stream turbulence characteristic inside the calculation domain. The difference between the cases with and without free-stream turbulence, whose intensity is up to 2.2% of mean free-stream velocity, is not observed clearly on the mean and instantaneous value fields in the present calculation.