A structure for an underwater sound absorber with subwavelength thickness and a quasi-perfect absorption property at multiple frequency bands is reported. This absorber consists of a viscoelastic coating layer embedded with periodically distributed plate scatterers (PSs). The embedded PSs cannot only slow sound waves in the coating, leading to a down-shifted resonance frequency where the absorption is maximized, but also introduce multiple local bending modes and local longitudinal modes in the coating. Via proper selection of the parameters of the PSs and the PS array, multiple local resonance modes of different types in a coating unit can be excited, resulting in quasi-perfect absorption of incident sound at multiple frequencies whose wavelengths are much longer than the thickness of the coating layer. For example, absorption (89%) of underwater sound at 462.9 Hz is achieved by such a layer with a thickness of 6 cm, which is 1.9% of the wavelength of the incident sound. Broadband quasi-perfect absorption can also be realized by coupling of those multiple local resonant modes. This quasi-perfect absorption property can also be observed for sound waves with different incident angles, because a large number of local intrinsic modes could still be excited.