Magnetorheological elastomers (MRE), a new type of smart material, overcome the disadvantages of magnetorheological fluid such as particle sedimentation and instability. The MRE smart material takes the place of the conventional viscoelastic material creatively, and the magnetic circuit analysis of a new viscoelastic damper with adjustable stiffness is proposed. According to the scheme determined through theoretical analysis, a viscoelastic damper with adjustable stiffness is designed, whose maximum output force reaches 15 kN, and its performance experiment is carried out on the hydraulic loading device, indicating that the new type damper has a continuously adjustable shear stiffness with current change. Finally, the revised Kelvin model is established for the new type damper, and the effectiveness of the model is proved through the comparison between the model simulation results and experimental results.