Abstract: Near-space high-speed flows involve cross-scale effects spanning from continuum regimes to rarefied regimes. Conventional linear constitutive relations based on Newton's law of viscosity and Fourier's law of heat conduction may be inadequate for describing the nonlinear coupling effect between stress and heat flux under nonequilibrium conditions. In this paper, the nonlinear coupled constitutive relations (NCCR) were solved using a hybrid iterative method which combines the advantages of fixed-point iteration and Newton iteration. The governing equations were discretized by a finite-volume method on structured grids, and the LU-SGS implicit scheme was employed to accelerate convergence. Comparative computations and analyses between the NCCR model and the Navier-Stokes(N-S) equations were performed for the HyTRV lifting-body vehicle under various altitudes (30, 60, 90 km), Mach numbers (5–20), and angles of attack (0°–20°). The results indicate that at altitudes of 30 km and 60 km, the primary flowfield structures and surface pressure coefficient distributions predicted by the two models are pressure coefficient. At 90 km and Mach 20, the pressure and heat-flux peaks predicted by NCCR are notably lower than those of the NS solutions, and the discrepancies further increase with the angle of attack. The findings of this study can serve as a reference for the aerodynamic and aerothermodynamic characterization of high-speed lifting-body vehicles over a wide range of altitudes and Mach numbers.