In this article, the double decomposition method is used to analyze the annular hyperbolic profile fins with variable thermal conductivity. The double decomposition method is an advantageous way to solve the nonlinear problem. The solution gained by the double decomposition method is in the form of infinite power series, and the variable thermal conductivity is considered to have a linear relation with temperature. The results from the exact model solution are compared with the constant thermal conductivity case. The parameters that affect the fin performance and temperature distribution strongly are identified.