State-to-state (StS) model and multi-temperature (MT) model are used to numerically simulate the high-temperature air flow behind normal shock waves. In the StS model, each vibrational state of neutral molecules and electronic excited states of neutral atoms were regarded as pseudo species. MT model described the different modes of internal energy with translational–rotational temperature, the vibrational temperatures of every neutral molecules and electron–electronic excitation temperature specifically. The simulations with freestream speeds range from 5 to 11 km/s are carried out. The results indicate that there are obvious under-population of the high-lying vibrational and electronic states in the near shock region, which are caused by the rapid dissociation and ionization processes respectively. As compared with StS model, in MT model the vibrational and electronic excitation, chemical reactions take place later, the flow attains thermal equilibrium later while attains chemical equilibrium earlier. The vibrational energy loss caused by chemical reactions is less and the electronic energy loss through the impact ionization reactions is more predicted by the MT model, and the specific temperatures cannot correctly describe the non-equilibrium vibrational and electronic population distribution.