Excessive vibration has always been a serious problem for conical shell structures, while the application of the graphene-based free-constrained layer (GFCL) based on carbon fiber-reinforced composite (CFRC) structure is a novel way to improve structural performance. An analytical model for vibration and dynamic characteristics of the GFCL-CFRC conical shell resting on the Winkler-Pasternak elastic foundation with arbitrary boundary conditions is constructed, and four types of GFCL porosity distribution and GFCL dispersion pattern are considered in this model. The multi-segment technique and virtual spring technique are utilized to simulate arbitrary boundary conditions. Then, the first-order shear deformation theory (FSDT) and Hamilton's principle are employed to obtain the motion equation of the GFCL-CFRC conical shell, and the motion equation of the GFCL-CFRC conical shell is solved by the Ritz method. In conclusion, the dispersion mode of GFCL, thickness ratio of GFCL, and fiber angle have influence on the dynamic performance. With a reasonable design, the dynamic performance of the GFCL-CFRC conical shell can be further improved.