A practical approach is implemented for thermal stresses in an axisymmetric thin annular fin, made of functionally graded material. All material properties of the annular fin are assumed to be graded along the fin radius as a power-law function. A linear differential equation is derived to be the governing equation. Analytical solution of such equations except for simple grading functions is difficult or maybe not possible to implement for each parameter, so the numerical approach becomes inevitable. The novelty of the present study is to introduce the effects of mechanical and thermal properties on the thermal stress distribution of functionally graded annular fin with the help of a complementary function method (CFM). The complementary functions method will be incorporated into the analysis to convert the problem to an initial value problem, which can be easily solved by, for instance, Runge-Kutta methods with great accuracy. The results are validated for isotropic and homogeneous annular fin.