A skin cloak based on the acoustic metasurface made of graded spiral units is proposed and numerically investigated. The presented skin cloak is an acoustical layer consisting of 80 subwavelength-sized unit cells, which provide precise local phase modulation and hence resort the disturbed sound filed in such a way to hide the object to acoustic wave. Numerical simulations show that the suggested skin cloak both work well under normal and small-angled incidences. By taking the advantage of the spiral-typed metasurface, the suggested skin cloak is rather thin with thickness in the order around 1/7 of the wavelength of target frequency, moreover, the intrinsic characteristics of modest dispersion ensure the skin cloak provides remarkable acoustic invisibility in a broad frequency ranging from 2500 Hz to 3600 Hz.