An analytical-numerical method is presented for analyzing dispersion and characteristic surface of waves in a circular cylinder composed of functionally graded piezoelectric material (FGPM). In this method, the FGPM cylinder is divided into a number of annular elements with three-nodal lines in the wall thickness. The elemental mechanical as well as electrical properties are assumed to vary linearly in the thickness direction so as to better model the spatial variation of the mechanical and electrical properties of FGPM. The associated frequency dispersion equation is developed and the phase velocity and slowness as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. The calculation examples provide a full understanding of the complex phenomena of elastic waves in FGPM cylinders.