New Reddy-type elements based on Reddy’s higher-order theory are used in the analysis of composite sandwich plates with viscoelastic core, which is achieved by considering independent transverse displacements on two faces and linear variations through depth of plate core. In addition, Young modulus, rotational inertia, and kinetic energy of core are considered and core is assumed as 3D elastic structure with the properties of an orthotropic viscoelastic material. To improve the Reddy’s higher-order theory, a rectangular element with four nodes, which each node has seven degrees of freedom, is proposed. Hamilton’s principle has been used to obtain the equations of motion. A finite element code for structural response analysis of the free vibration is developed. The obtained results are compared with existence researches. The influence of material properties, lamination schemes, and fiber angle on natural frequencies of composite plates are investigated.