The present study aims to provide a deeper understanding for the transient thermal stress distributions of an annular fin made of FGM. The material properties of annular fin are assumed to be graded along the fin radius as a power-law function while the Poisson's ratio is taken to be constant for simplicity. The energy balance equation is solved on Laplace domain by using exponential like solution introduced by Keller and Keller and Gauss quadrature method. The transformation to time domain achieved by using Durbin fast Fourier transformation method. The temperature distribution and thermal stresses are presented in graphical form for FG annular fin that is pure ceramic in the base and pure metal on the tip.