A direct numerical simulation of a spatially developing turbulent boundary layer was performed at a freestream Mach number of 7.21, with a wall-to-recovery temperature ratio of 0.53. The Reynolds number based on the momentum thickness ranged from Reθ = 5390 at the inlet to Reθ = 7160 at the outlet of the computational domain. An auxiliary DNS was conducted first using the digital filtering method as inlet boundary condition to generate a fully develop turbulence. Then, the primary DNS was performed using the auxiliary DNS data of the spanwise-wall-normal plane at δin = 7 mm as the inflow boundary condition. The basic turbulent statistics were analyzed, including the temperature–velocity relation, turbulent intensities, the strong Reynolds analogy, and the turbulent kinetic energy budget. The results demonstrate good agreement with experimental data and other DNS studies in a similar freestream flow condition.