Abstract The present work deals with the dynamics properties of two kinds of multi-layered composite sandwich doubly-curved shells with two-layered viscoelastic cores based on first order shear deformation theory (FSDT). The Hamilton’s principle is adopted to deduce the equations of motion that govern the free vibrations of the sandwich doubly-curved shells. The vibration frequencies and associated loss factors of shells are obtained by solving these equations as an eigenvalue problem based on the Navier method. Then, the validity of present solutions is confirmed comparing with those available in the published literatures. Next, the change rules of frequencies and loss factors with structural parameters are evaluated and presented graphically. New results for dynamics properties of multi-layered composite sandwich doubly-curved shells with two-layered soft cores are proposed for the first time.