A type of light absorber made of continuous layers of metal and dielectric films is studied. The metal films can have thicknesses close to their skin depths in the wavelength range concerned, which allows for both light transmission and reflection. Resonances induced by multiple reflections in the structure, when combined with the inherent lossy nature of metals, result in strong absorption spectral features. An eigen-mode analysis is carried out for the plasmonic multilayer nanostructures which provides a generic understanding of the absorption features. Experimentally, the calculation is verified by a reflection measurement with a representative structure. Such an absorber is simple to fabricate. The highly efficient absorption characteristics can be potentially deployed for optical filter designs, sensors, accurate photothermal temperature control in a micro-environment and even for backscattering reduction of small particles, etc.