A simple method for obtaining higher‐order solutions of a solitary wave is presented. The method is based on the higher‐order approximation of the reductive perturbation method. As a model equation, the Korteweg–de Vries (KdV) equation with fifth‐order dispersion term is employed and higher‐order solutions are obtained. In the case of ion‐acoustic solitary wave, the fourth‐order solution is given explicitly and is compared with numerical solutions. The fourth‐order solution is shown to be valid if a normalized wave amplitude is less than 0.5.