A kind of fiber-optic acoustic sensor based on the multi-layered graphene material is studied, which has a Fabry-Perot interferometic cavity structure, consisting of single mode fibers and multi-layered graphene films. With the multi-layered pure graphene and multi-layered graphene oxide (GO) as the acoustic pressure sensitive film respectively, the experiments of acoustic wave sensing are conducted. The results indicate that, in the audio range, the average signal-to-noise ratios of the fiber-optic acoustic sensors based on multi-layered pure graphene and multi-layered GO films reach 56 dB and 69 dB, respectively. The sensitivities of the average minimum detectable acoustic pressure are 20.8 μPa·Hz-1/2 and 6.63 μPa·Hz-1/2, respectively, far smaller than that of the electric acoustic sensor. The fiber-optic acoustic sensors based on the graphene material possess a high sensitivity, which is suitable for the micro-acoustic pressure measurement under the environment of severe electromagnetic interference and confined spaces.