At present, there are fewer studies on the macroscopic mechanical hysteresis model of magnetically controlled smart magnetorheological elastomer (MRE), which is not conducive to the application control of MRE materials. To improve the control effect of MRE materials, an experimental study on MRE's magnetostrophic shear mechanical properties based on the Bouc-Wen model was conducted. The influence of magnetic field strength on the mechanical parameters of MRE was analyzed. Firstly, with the assistance of Simulink to establish the Bouc-Wen simulation model was established for MRE parameter fitting. Then, the stiffness, damping, and other material parameters were analyzed with the magnetic field strength change rule. Finally, through the experiments, the model validity was examined. The results show that with the increase of magnetic field strength, the parameters of MRE energy storage and energy consumption have different degrees of increase, in which the equivalent stiffness and maximum damping force increase significantly, respectively, increase 210.61%, 205.41%. In the range of 0.5 ~ 0.7 T magnetic field parameter growth rate is faster in the range of 0.7 ~ 1.0 T growth tends to be saturated. The dynamic mechanical properties of MRE are better described by the Bouc-Wen model, and the maximum error of the characteristic parameters is 4.42%. The research results can provide theoretical and experimental references for the optimal preparation and algorithmic control of MRE materials.