In this paper, air chemical non-equilibrium effects on the shock-induced combustion flow are numerically investigated for a reaction control system (RCS) with gaseous ethylene fuel by solving multi-component Navier-Stokes (N-S) equations. An integrated numerical method is developed that considers two different chemical reaction mechanisms: the high temperature air chemical non-equilibrium reactions and ethylene-oxygen combustion reactions. The method is independently validated by two types of reacting flow: the hypersonic air chemical non-equilibrium flow over a sphere and supersonic ethylene-oxygen combustion flow for a dual combustion chamber. Furthermore, the mixed reacting flow over a blunt cone with a transverse multi-component gaseous jet is analyzed in detail. Numerical results indicate that air chemical non-equilibrium effects could lead to a reduction of the shock detachment distance, a decrease of the temperature behind the shock wave and a reduction of the combustion products.