This study analyzes and predicts the vibration characteristics of fiber-reinforced composite sandwich (FRCS) cylindrical-spherical (CS) combined shells with hexagon honeycomb core (HHC) for the first time based on an analytical model developed, which makes good use of the advantage of the first-order shear deformation theory (FSDT), the multi-segment decomposition technique, the virtual spring technology, the Jacobi-Ritz approach, and the transfer function method. The equivalent material properties of HHC are firstly determined by the modified Gibson’s formula, and the related energy equations are derived for the HHC-FRCS-CS combined shells, from which the fundamental frequencies, the mode shapes, and the forced vibration responses are solved. The current model is verified through the discussion of convergence and comparative analysis with the associated published literature and finite element (FE) results. The effects of geometric parameters of HHC on the dynamic property of the structure are further investigated with the verified model. It reveals that the vibration suppression capability can be greatly enhanced by reducing the ratio of HHC thickness to total thickness and the ratio of wall thickness of honeycomb cell to overall radius, and by increasing the ratio of length of honeycomb cell to overall radius and honeycomb characteristic angle of HHC.