The strain sensitivity of bare fiber grating under the action of acoustic wave is too low, which is difficult to detect the effective reflection wavelength change. In this paper, the longitudinal sensing of fiber grating is used as a model, and a layer of thickness far exceeding the inner diameter of the fiber is coated around the grating. Low Young's modulus cylindrical coating is used to increase the strain sensitivity of the fiber grating. We also use the linear region of the reflection spectrum of the phase-shift grating as the edge of the edge filtering method to improve the sensitivity of laser detection. Transmission matrix method is then applied in the simulation to analysis the reflection spectrum of grating and reflectance curve of laser. The simulation results show that the strain sensitivity of the longitudinal sensing model of acoustic wave is better than that of the transverse sensing model. The coating layer with low Young's modulus can significantly improve the strain sensitivity of the grating. Under the action of acoustic wave with frequency lower than 1.7 kHz.The longitudinal sensing sensitivity of the fiber grating coated with polyurethane coating reaches 6.1 nm/MPa, which is 381 times higher than that of the bare fiber grating. Combined with the phase-shift grating reflection spectrum linear region, the comprehensive sensitivity is improved by 2 203.6 times, effectively improving the acoustic wave detection sensitivity of the grating.