Fins are essentially used in diverse engineering applications to increase the heat transfer between the hot and cold media. In this paper, a technique for computing the analytic approximate solution of the nonlinear differential equations resulting from heat transfer problems, in particular through fins, is developed. The simplicity of the approach presented here is due to its base functions, which makes this method straightforward to apply and formulate without any need for discretization. Analysis of the error and comparisons with the other methods are presented. A few physically interesting fin problems of heat transfer are treated to illustrate that the proposed algorithm generates highly accurate solutions.