The numerical simulation for the hydrogen jet experiments performed by Schefer et al., is conducted using the compressible, multicomponent Navier-Stokes equations with the preconditioning method. The simulated results for the hydrogen jet agree with the theoretical results of Tollmien. As far as comparing with the experiments by Schefer et al., the concentration profiles along the radial direction agree with the present numerical results and that along the centerline also agree well with the experimental results after the data are normalized by the equivalent nozzle diameter. It is confirmed that the spread of the jet width from the jet exit to downstream is affected by the Kelvin-Helmholtz instability. It is also confirmed that the jet flow field is formed alternately by the high pressure region and the low pressure one to cause the jet flow fluctuation.