A numerical study on mixing of air and hydrogen is performed by solving two-dimensional full Navier-Stokes equations. The main stream is air of Mach 5 entering through the configured inlet of the combustor and gaseous hydrogen is injected from the configured jet on the side wall. Supersonic mixing and diffusion mechanisms of a transverse hydrogen jet in two-dimensional finite air streams have been analyzed and discussed. The computed results are compared with the experimental data and show good agreement. For an otherwise fixed combustor geometry, the air inlet width and injection angle are varied to study the physics of mixing and flow field characteristics. On the effect of inlet width variation, two competing phenomena have been observed: (i) upstream of injector the strength of recirculation is higher for wider inlet and consequently the mixing increases, and (ii) downstream, the diffusion of hydrogen decreases with the increase of inlet width and eventually mixing decreases. As a result, in far downstream the mixing efficiency increases up to certain inlet width and then decreases for further increment of inlet width. For the variation of injection angle results show that upstream of injector the mixing is dominated by recirculation and downstream the mixing is dominated by mass concentration of hydrogen. Upstream recirculation is dominant for injecting angle 60° and 90°. Incorporating the various effects, perpendicular injection shows the maximum mixing efficiency and its large upstream recirculation region has a good flame holding capability.