The unsteady process of ignition and combustion of ethylene at varied fuel/air equivalence ratios in a Mach 2.5 supersonic model combustor is studied numerically. The reacting turbulent flow is solved using the shear stress transport (SST) k turbulence model and a reduced kinetic mechanism obtained with sensitivity analysis and the assumption of quasi-steady-state from a detailed mechanism of ethylene. The present results reveal that ignition of ethylene first takes place in the cavity due to the local low speed and high static temperature. At a low equivalence ratio of 0.32, combustion is established and stabilized downstream of the cavity. However, as the equivalence ratio increases to 0.6, the combustion downstream of the cavity generates sufficient heat release to cause pressure and the flame to propagate upstream and to generate a shock train upstream of the injection point. Formation of the shock structure results in subsonic flow in the vicinity of the injection and combustion with higher efficiency stabilized mainly in the fuel/air mixing shear layer. The time evolutions of fuel jet and C2H2 qualitatively agree well with the experimental results, of which high-speed schlieren photos and chemiluminescence images of CH* are obtained at similar flow conditions.