Turbulent mixing field of hydrogen jets injected in supersonic streamwise vortices was numerically investigated using large-eddy simulation (LES). The jet and the streamwise vortices were introduced in a similar and simplified manner to those introduced by the alternating-wedge (AW) strut injector. The LES reproduced the large-scale wavy jet structure containing small-scale vortices as those observed in the past experiment of the AW strut. The streamwise vortices strongly promoted the jet spreading and the turbulent transition. Downstream of the turbulent transition, the fully developed turbulent state was achieved in the wavy jet structure. The instantaneous and time-averaged mixing efficiencies were quantitatively evaluated and compared each other to investigate the intermittency of mixing state. The mixing efficiency rapidly increased by the turbulent transition. The jet mixing in the streamwise vortices had lower intermittency compared to the transverse jet from the wall. The effects of the incident shock wave across the hydrogen jet were also investigated in detail. The turbulent properties such as the fluctuation intensity and the power spectrum hardly changed by the crossing of oblique shock wave. The mixing efficiency slightly increased after the oblique shock wave passed through the hydrogen jet.