Abstract: Direct numerical simulation (DNS) of turbulent flat-plate boundary layer flows with free-stream Mach numbers of 2.25 and 6 are performed, and the data are validated by compared with theoretical, experimental and numerical results. Based on the DNS data, turbulence models (including k-ε varepsilon model, SA model and BL model) are assessed. For Mach 2.25 case, numerical results show that the realizable k-ε varepsilon model agrees the DNS data very well and the turbulent viscous coefficient of the classical k-ε varepsilon model is higher than that of the DNS data. SA model gives quite good turbulent viscous in the inner layer of the boundary-layer, but it gives higher turbulent viscous in the outer layer. For high Mach number case, k-ε varepsilon models and SA model overestimate turbulent viscous coefficient. In Mach 6 case, BL model cannot give good interface location between the inner and the outer layer. To improve the BL model, the authors modify the coefficients, and the new model's viscous coefficient agrees well with the DNS data.