In the present work, the numerical study of the transient thermal response of a composite trapezoidal annular fin assembly is investigated. The fin assembly coated with a face material of different thermal characteristics involving nonuniform convective heat transfer to the enviornment is also examined. Numerical solutions are obtained by using the finite difference method. In order to solve the system of algebraic equations, the modified strongly implicit procedure has been utilized. Therefore, the temperature distribution and the heat flux through the supporting wall are calculated. It is shown that the isothermal lines of the fin assembly are two-dimensional variations. Moreover, the heat flow through the fin assembly increases as the tube thickness increases, the thickness of the face layer decreases, the Biot number B(subscript if) increases, or B(subscript i) decreases.