In this study, the large-amplitude vibration of a functionally graded (FG) truncated conical shell with an initial geometric imperfection has been investigated using large deformation theory with a von Karman-Donnell type of kinematic nonlinearity. The material properties of an FG truncated conical shell are assumed to vary continuously through the thickness. The fundamental relations, the modified Donnell-type nonlinear motion, and compatibility equations of the FG truncated conical shell with an initial geometric imperfection are derived. The relation between nonlinear frequency parameters with the dimensionless amplitude of imperfect FG truncated conical shells is obtained. Finally, the influences of variations of the initial geometric imperfection, compositional profiles, and shell characteristics on the dimensionless nonlinear frequency parameter and frequency-amplitude relations are investigated. The present results are compared with the available data for a special case.