Magnetorheological elastomer (MRE), known as a smart material, whose mechanical properties can be changed with external magnetic fields. The aim of this paper is to present results of studies on magnetoviscoelasticity properties of the new developed MRE consisting of carbonyl iron particles displaced in the matrix made of a bromobutyl rubber. The MRE samples are fabricated in a constant magnetic field. These MRE specimens are experimented in the shear mode to investigate the dynamic viscoelastic properties under sinusoidal loadings with different displacement amplitudes and frequencies. The tests of each loading case are carried out in four different magnetic field strengths from 0mT stepwise to 300mT. The results of dynamic properties of MRE samples are obtained in terms of experimentally determined shear storage modulus and loss factor. These results demonstrate that the MREs have properties of variable stiffness and high loss factor.