The damping properties analysis of composite sandwich doubly-curved shells (CSDCS) is presented in this paper. First, based on the Hamilton's principle, governing equations of CSDCS are developed by applying the first-order shear deformation shell theory. Because the rotary inertias and shear deformation of all layers are taken into account, thin-to-moderately thick doubly-shells can be studied. Next, these equations are solved by means of the closed-form Navier method. The accuracy of the solution is validated by comparing its results with those available in the literature. Finally, the variation of modal loss factor with system parameters is evaluated and presented graphically, and optimal damping properties of CSDCS are obtained by analyzing the influence of the geometrical parameters as well as the physical parameters on damping properties.