In order to describe the close-in flow field characteristics and the propagation of shock wave of spherical TNT charge bursting in real air, the special features of air under high temperature and high pressure are taken into account and a complete set of dimensionless hydrodynamic equations in Lagrangian distance coordinate system is established by using the state equations of real air. After that, a set of transformed hydrodynamic equations in shock moving coordinates is employed to simplify the numerical calculation. Combining the artificial viscosity technique and shock fitting technique, a method for calculating the whole flow field of TNT bursting in real air is developed. As an example, the calculation results are in good agreement with the existing literature, and experiments data shows that the theory established in this paper is suitable for describing the close-in characteristics and calculating shock wave propagation in distance region of TNT charge bursting in real air.