A new design of adaptive tuned vibration absorber was proposed in this study for vibration reduction. The innovation of the new absorber is the adoption of the eccentric mass on the top of the multilayered magnetorheological elastomer (MRE) structure so that this proposed absorber has two vibration modes: one in the torsional direction and the other in translational direction. This property enables the absorber to expand its effective bandwidth and to be more capable of reducing the vibrations especially dealing with those vibrations with multi-frequencies. The innovative MRE absorber was designed and tested on a horizontal vibration table. The test results illustrate that the MRE absorber realized double natural frequencies, both of which are controllable. Inertia's influence on the dynamic behavior of the absorber is also investigated in order to guide the design of the innovative MRE absorber. Additionally, the experimentally obtained natural frequencies coincide with the theoretical data, which sufficiently verifies the feasibility of this new design. The last part in terms of the vibration absorption ability also proves that both of these two natural frequencies play a great role in absorbing vibration energy.