In order to break through the bottleneck of narrowness of the local resonance band-gap (LRBG) and obtain wide band-gaps in low frequencies, we apply the local resonator based on magnetorheological elastomer (MRE) to the design of the new metamaterial beam. In this paper, the spectral element method is used for modeling and calculation. Based on the discrete Fourier transform theory and the variational method, the spectral beam element is constructed. According to the force-displacement relationship method, the spectral element of the local resonator is established. The correctness of the results in this paper is validated by the convergence of the finite element method results. The influences of the applied magnetic field, the mass of the local resonator and the material combination of the beam in a cell on the band-gap property are discussed and analyzed. It is found that the metamaterial beam designed by the local resonator based on MRE can effectively increase the bandwidth of LRBG, which is comparable to that of the Bragg band-gap (BBG), and can improve the vibration isolation performance. With the increase of the local resonator mass, the lower bound frequency of the BBG decreases while the bandwidth increases. Increasing the unit-cell number of the MRE metamaterial beam is an effective means to improve the attenuation properties of the BBG and LRBG. The larger the difference of the material combination is, the more the band-gaps in low frequency are, the larger the total bandwidth of band-gaps and the stronger the attenuation capability become.