The dynamic stability of sandwich annular plate with an electrorheological (ER) fluid core and constraining layer are studied. The annular plate is covered an electrorheological fluid core layer and a constraining layer to improve the stability of the system. The discrete layer annular finite element and the harmonic balance method are adopted to calculate the boundary of instability regions for the sandwich annular plate system. Besides, the rheological property of an electrorheological material, such as viscosity, plasticity, and elasticity can be changed when applying an electric field. When the electric field is applied on the sandwich structure, the damping of the sandwich system is more effective. Thus, variations of the instability regions for the sandwich annular plate with different applying electric fields and thickness of ER layer are presented and discussed in this study. The ER fluid core is found to have a significant effect on the location of the boundaries of the instability regions.