This paper focuses on the vibration analysis of three-layered curved sandwich beams with elastic face layers and viscoelastic core. First, the equations of motion that govern the free vibrations of the curved beams together with the boundary conditions are derived by using the principle of virtual work, in the most general form. Then, these equations are solved by using the generalized differential quadrature method in the frequency domain, for the first time to the best of the authors' knowledge. Verification of the proposed beam model and the generalized differential quadrature solution is carried out via comparison with the results that already exist in literature and the ANSYS finite element solution combined with the modal strain energy method. The effect of system parameters, i.e. layer thicknesses, the lamination angle of layers and the curvature on the vibration and damping characteristics of a curved sandwich beam with laminated composite face layers and a frequency dependent viscoelastic core is investigated in detail.