An analytical model is established to investigate free vibration characteristics of composite laminated conical-cylindrical coupled shell under arbitrary boundary conditions. In the present approach, artificial spring technology is adopted to simulate arbitrary boundary conditions and continuity conditions. The displacement admissible functions are described using the spectro-geometric method (SGM). Then, the dynamic governing equation related to free vibration of the composite laminated coupled shell are obtained within the framework of the first order shear deformation theory (FSDT) and the spectro-geometric method and solved numerically by means of the Rayleigh-Ritz method. The convergence and accuracy of the presented model is demonstrated by comparing the present results with those from the published literature and finite element method (FEM). In addition, the influences of the elastic modulus ratio and thickness on the free vibration characteristics of composite laminated conical-cylindrical coupled shell are also analyzed.