The low-frequency underwater sound absorption phenomenon induced by the localized resonance in phononic crystal shows a promising application for the design of underwater acoustic absorption material in recently study. To further reveal the sound absorption mechanism and optimize the low-frequency underwater sound absorption characteristic, the viscoelastic coating embedded with various shapes of scatterer is investigated. In this paper, to shorten the computing time of the original finite element program and save the core memory, the conventional finite element method is simplified due to the symmetry of the lattice and the scatterers, then the simplified finite element method is validated by comparing the results of the simplified finite element method with those of the conventional finite element method. The relationship between the resonance mode described with the displacement contours of one unit cell at specified frequencies and the corresponding absorption spectrum is discussed in detail, which reveals briefly the sound absorption mechanism of the viscoelastic coating embedded with cylindrical scatterer. Finally, the shape effect of the scatterer on the sound absorption characteristics is investigated, spherical scatterers and the three cylindrical scatterers with different shapes but the same volume are considered. Further, the influence of the density of the core on acoustic absorption characteristic under an air backing is discussed. The results show that lower sound absorption properties can be deduced by adopting the cylindrical scatterers and reducing the radius of the base of circular cylindrical scatterer, and the absorption bandwidth can be improved by choosing the optimal scatterer material.