Adomian’s decomposition method (ADM) is a nonnumerical method which can be adapted for solving nonlinear ordinary differential equations. In this paper, the principle of the decomposition method is described, and its advantages as well as drawbacks are discussed. Then an aftertreatment technique (AT) is proposed, which yields the analytic approximate solution with fast convergence rate and high accurscy through the application of Padé approximation to the series solution derived from ADM. Some concrete examples are also studied to show with numerical results how the AT works efficiently.