This paper presents an analysis of the wave dispersion of a smart cylindrical shell that is composed of a graphene-reinforced nanocomposite (GRNC) at the top of the shell, functionally graded piezo magnetic material (FGPMM) at the bottom of the structure, and an auxetic core in the center of the shell. When calculating the displacement field of a smart shell, the first shear deformation theory is used as an assumption. In addition, the governing equations of the smart sandwich shell may be derived by using Hamilton's principle and Maxwell's law to determine the electrical and magnetic potential. Therefore, the phase velocity of a cylindrical sandwich shell may be calculated by applying exponential functions to the solution of the governing equations to get the desired result. Last but not least, the phase velocity of a smart shell is represented based on the geometrical parameters such as the thicknesses of the FGPMM layer, the GRNC layer, and the Auxetic core, as well as the physical parameters such as the Winkler foundation, temperature change, FG power index, magnetic potential, and external electric voltage that is shown in each figure.