In this paper, the vibration and stability of a three-layered conical shell containing a functionally graded material (FGM) layer subjected to axial compressive load are studied. The material properties of the functionally graded layer are assumed to vary continuously through the thickness of the shell. The variation of properties follows an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the dynamic stability and compatibility equations of three-layered truncated conical shells containing an FGM layer are obtained first. Applying Galerkin's method, these equations are transformed to a pair of time dependent differential equations, and critical axial load and frequency parameter are obtained. The results show that the critical parameters are affected by the configurations of the constituent materials and the variation of the shell geometry. Comparing results with those in the literature validates the present analysis.