The turbulent flow past a simplified Intercity-Express 3 high-speed train at ReH=6×104 is investigated by a combination of wind tunnel experiments and numerical simulations using the large-eddy simulation (LES), the improved delayed detached eddy simulation (IDDES) and the unsteady Reynolds-averaged Navier-Stokes (URANS) simulation. This work aims to compare the predictive capabilities of LES, IDDES and URANS for the flow over a streamlined high-speed train. Numerical simulations are compared to experimental data for validation. Results show that the well-resolved LES is more accurate among the numerical methods used. Compared to the well-resolved LES, IDDES and URANS using the coarser mesh can produce similar mean flow, although IDDES and URANS are found to be slightly inaccurate for the coherent wake structures near the wall. However, for the near-wall flow instability concerning wake dynamics, Reynolds stresses, turbulence kinetic energy and the fluctuation of pressure, IDDES is found to be inapplicable. Overall, this study suggests that the well-resolved LES is appropriate to the flow of a streamlined high-speed train. Moreover, IDDES and URANS are proved to apply to the mean field of the studied flow.