<p>This paper first provides a novel model for free vibration analysis of the functionally graded graphene platelets reinforced composite (FG-GPLRC) truncated smart sandwich conical shell with variable thickness. The simply supported smart sandwich structure consists of two magneto-electro-elastic face sheets made of BaTiO₃–CoFe₂O₄ and a longitudinally varying thickness FG-GPLRC core with four distinct distributions. The effective material parameters of the FG-GPLRC core are determined by the improved Halpin–Tsai approach and the rule of mixture. Considering the coupling effect of elastic, thermal, electric and magnetic fields, the constitutive relations and laminated constitutive relations are formulated. Adopting the Reddy’s third-order shear deformation theory with zig–zag higher-order polynomials and Hamilton's principle, the governing equations of motion for the smart truncated sandwich variable thickness FG-GPLRC conical shell are identified. The natural frequencies of the shell are calculated by adopting the double trigonometric approximate series and Galerkin approach. The feasibility of the theoretical approach is validated by the comparative investigation. The impacts of the weight fractions and distribution types of graphene platelets (GPLs), the number of core layers, temperature increment, core layer’s maximum–minimum thickness ratio, semi-vertical angle, length-thickness ratio, minimum radius-thickness ratio and core-to-face sheet thickness ratio on the natural frequencies and modes are explored. The free vibration investigations provide a reference for the optimal design and further research of the smart FG-GPLRC variable thickness sandwich structures.</p>