Abstract: The prediction of boundary-layer transition is crucial for designing high-speed aircraft, yet high-fidelity high-speed transition prediction models with broad application prospects are still not available. While extensive efforts have been directed towards modifying the γ-Re_θ transition model, which has proven effective in low-speed flows, for its application in high-speed scenarios, these refined γ-Re_θ models continue to encounter challenges in attaining widespread application. To develop a more practical engineering transition model, we have implemented a high-speed correction to the γ-Re_θ transition model, leveraging the high-order WCNS platform. Firstly, we compared the performance of second and fifth-order schemes in simulating a high-speed flat-plate turbulent boundary layer. The results reveal that the higher-order scheme delivers more accurate results, even with a coarse grid, evidenced by its precise prediction of the skin friction coefficient. This underscores the importance of employing high-order schemes for discretizing the turbulence model. Then we refined the SST turbulence model, the transport equations of γ and Re_θ, as well as the turbulent Prandtl number (Pr_t), yielding results in line with experimental data in a wide range of Mach numbers, geometries, and wall thermal conditions. The obtained transition model exhibits not only high accuracy in predicting the transition position but also the aerodynamic force/heat downstream of the transition front. Finally, compared to the original γ-Re_θ transition model, the modified SST turbulence model can effectively improve the skin friction prediction accuracy in the turbulent area, and limited improvement on the transition location. Notably, the Ma-modified γ and Re_θ transport equations have significantly improved the prediction accuracy of the transition location. Furthermore, the modified Pr_t effectively improves the adiabatic wall temperature in transitional and turbulent regions but slightly improves the heat flux on isothermal walls.