The aim of this paper is to perform a structural optimization of composite beams with multilayered viscoelastic cores based on the first-order shear deformation theory. First, the numerical model of vibration governing equations is derived by employing the Hamilton's principle, and these vibration equations are solved by means of the closed-form Navier method. Then the calculated results are compared with the findings of previous literatures, and a good agreement is observed. Finally, structural optimization of composite sandwich beams is obtained by numerical analysis.