The supersonic mixing layer formed by a planar thin hydrogen jet at 2.3 Ma and a 2.0 Ma surrounding airflow in a scramjet engine model is studied in order to investigate the growth characteristics with consideration of shocks. Flow field structure and features of the supersonic mixing layer are achieved by using large eddy simulation method with the OpenFOAM software. Reasonable agreements are obtained between calculation and experiment in terms of flow field structure and component distribution. The component concentration, the thickness, the compressibility effect and the total pressure loss are analyzed. Results show that four developing regions can be observed for the growth of the mixing layer. The expansion-fan/shock-wave pattern at the injector exit makes the convective mach number decrease dramatically, leading to a reduction in compressibility effects and a contribution to the development of the mixing layer. The interaction of shock/mixing layer results in local amplification of turbulence and gain of vorticity, which is beneficial to the supersonic mixing. However, the increasement in total pressure loss is unavoidable in the presence of shocks because they can bring performance losses of the scramjet. Thus a tradeoff between the enhanced mixing efficiency and the decreased total pressure recovery should be considered in the scramjet optimization design.