The resonance shift property of magnetorheological elastomer is important for developing adaptive absorbers. However, it is well-known that passive nonlinear absorbers have wider effective frequency bandwidths. This article combines these two characteristics in order to develop a hybrid magnetorheological elastomer absorber which can shift its natural frequency and has a wider absorption bandwidth under each constant current. The adaptability and nonlinearity were fully verified experimentally. Afterwards, the absorption ability of the hybrid magnetorheological elastomer absorber was investigated and analyzed. The results show that the effective bandwidth of this absorber is broadened under certain levels of current than linear absorber, and this is caused by the presence of nonlinearity; and the adaptability induced by the magnetorheological elastomer undoubtedly empowers the absorber possible to trace the excitation frequency changing in real time. A short-time Fourier transform was finally used to control the magnetorheological elastomer absorber to verify its controllability, showing that an optimal absorption transmissibility was achieved by the controlled hybrid absorber.