In this study, acoustic metasurfaces are optimized to suppress the broadband frequencies of unstable modes in a Mach 6 boundary-layer (BL) flow. The metasurface is cut into five pieces, and the geometrical parameters of each piece are optimized to afford a comprehensive admittance response to the local frequencies of the first and second modes. It shows the designed broadband metasurface not only is advantageous for stabilizing disturbances above the metasurface region but also inhibits the fast growth rate of low-frequency disturbances on the downstream smooth wall.