This paper focuses the computational study of non-premixed combustion in a scramjet combustor. The wedge shaped strut injector was used in the combustion process. In order to investigate the flame holding mechanism of the wedge shaped strut in supersonic flow, the two-dimensional coupled implicit RANS equations, the standard k-ε turbulence model and the finite-rate/eddy-dissipation reaction model are introduced to simulate the flow field of the hydrogen fueled scramjet combustor with a strut flame holder under different conditions. The static pressure of the case under the engine ignition condition is much higher than that of the case under the cold flow condition. The reflection of shock waves improves the mixing of hydrogen with the stream of inlet air and thus increases combustion efficiency. The mass flow rate of air is optimized for the best performance of engine.