The conventional approximate optimization method, which uses the statistical design of experiments(DOE) and response surface method(RSM), can derive an approximated optimum results through the iterative process by a trial and error. The quality of results depends seriously on the factors and levels assigned by a designer. The purpose of this study is to propose a new technique, which is called a sequential design of experiments(SDOE), to reduce a trial and error procedure and to find an appropriate condition for using artificial neural network(ANN) systematically. An appropriate condition is determined from the iterative process based on the analysis of means. With this new technique and ANN, it is possible to find an optimum design accurately and efficiently. The suggested algorithm has been applied to various mathematical examples and a structural problem.