We report the design, simulation, and experimental testing of an acoustic metasurface made from an array of low-flow-sensitivity Helmholtz resonators (LFSHRs). The low flow-sensitivity of sound attenuation reflects two aspects, one is the low sensitivity of the impedance peak magnitude that is attributed to the increase of the flow velocity at the interface resulted from the stronger vortexes inside the multilayer-hole neck, and the other is the low sensitivity of the impedance peak frequency due to the increased acoustic mass from the strengthened cavity-main flow interaction. Using this metasurface, the increment of both the magnitude and frequency of the impedance peak caused by the increasing fluid flow could be reduced by more than 70.5% and 93.8% respectively compared with a Helmholtz resonator (HR), and could be further minimized by parameter optimization. This low-flow-sensitivity acoustic metasurface proposed has great potential applications for aerodynamic noise control.