As the Mach number increases, the local static temperature gradually approaches the characteristic gas vibration/dissociation temperature, and significant thermo-chemical relaxation processes occur. The thermo-chemical nonequilibrium phenomenona could affect the mixing and combustion process and become a factor that must be considered for scramjet design. In this paper, a large eddy simulation solver based on the two-temperature model is developed. The transfer terms between vibrational and trans-rotational energy are modeled by the Landau–Teller formulation and the vibrational-dissociation coupling is considered by adopting the Park model. Three sets of simulations based on the Hyshot Ⅱ engine configuration with different models were performed simultaneously to validate numerical methods and analyze results. The results reveal that the shock, cross-injection of fuel, and Prandtl-Meyer flow induce significant nonequilibrium regions. The vibration relaxation process in the jet mixing region is frozen, the vibration temperature is much higher than the trans-rotational temperature, and the extra energy is converted from the vibration mode to the trans-rotational mode, resulting in the increase of the trans-rotational temperature and the advance of auto-ignition in the nonequilibrium condition. Considering the vibration-dissociation coupling, the higher vibration temperature promotes dissociation. It inhibits the generation of active radicals in the ignition process, weakening the enhancement effect of nonequilibrium on auto-ignition. In the expanded nozzle, the concentrations of molecules and trans-rotational temperature in nonequilibrium cases are slightly lower than those in the equilibrium case due to the enhancement of dissociation.