The numerical simulations on the high-pressure hydrogen jet are performed by using the unsteady threedimensional compressible Navier-Stokes equations with multi-species conservation equations. The present numerical results show that the highly expanded hydrogen free jet observes and the distance between the Mach disc and the nozzle exit agrees well with the empirical equation. The time-averaged H2 concentration of the numerical simulations agrees well with the experimental data and the empirical equation. The numerical simulation of ignition in a hydrogen jet is performed to show the flame behaviour from the calculated OH isosurface. We predicted the ignition and no-ignition region from the present numerical results about the forced ignition in the high-pressurized hydrogen jet.