The purpose of this paper is to investigate the effect of impinging oblique shock on combustion efficiency of hydrogen injection into the supersonic cross-flow. The two dimensional finite volume solver is developed to simulate the reacting flow, and the one-equation Spalart-Allmaras turbulence model is implemented to capture the turbulent flow characteristics. The impinging oblique shock is produced by a wedge that is located in the upper boundary of the flow field. Finding the best effective parameters on the combustion efficiency may lead to optimize the supersonic combustion chambers, from technological viewpoints. The variation of combustion efficiency versus various induced shock's collision positions with bottom wall in related to the fuel injection location is presented. In addition, the effect of induced shock strength on combustion process is investigated by changing the wedge's angle. Augmentation an additive, H2O2, to the fuel is the other parameter whose effect on combustion characteristics is studied in the disturbed field by impinging oblique shock. Finally, the effects of fuel injection angle as a predominant factor in flow and combustion features