This paper focuses on the vibration and damping analysis of three-layered sandwich cylindrical shells with stiff composite face layers and a viscoelastic core. The equations of motion and boundary conditions governing the free vibration are derived by using the Hamilton's principle. Then, generalized differential quadrature method is used to solve these equations to obtain the natural frequencies and modal loss factors. Results are validated against the ones that already exist in the literature and performed finite element method analyses of current study. In addition, a parametric study is performed for a sandwich shell with carbon fiber reinforced plastic face layers and a frequency dependent viscoelastic core. A 10-parameter fractional derivative model is used to represent the viscoelastic behavior of the core layer. The effects of system parameters, that is, layer thicknesses, the orientation angle of the face layers, and the subtended angle on the vibration and damping characteristics of open cylindrical shells, are investigated in detail. The vibration and damping analyzes of sandwich shells with frequency-dependent viscoelastic core are performed for the first time to the best of the authors' knowledge.