In this study, the finite element analysis of polar orthotropic annular plate with an electrorheological (ER) fluid core and constraining layer is investigated. The equations of motion of the polar orthotropic annular sandwich plate are derived by using the discrete layer finite element method. The extensional and shear moduli of the electrorheological fluid layer are described by the complex quantities. When applying an electric field, the rheological property of the electrorheological fluid materials, such as viscosity, plasticity, and elasticity can be changed. The damping of the sandwich system is more effective when the electric fields are applied on the system. The ER fluid core is found to have a significant effect on the vibrational behaviors of the sandwich annular plate and the characteristics of the sandwich system can be controlled actively. Additionally, the effects of ER layer thickness, base annular plate stiffness, and some designed parameters on natural frequencies and modal loss factors are also discussed in this paper.