Abstract In time series analysis, we often find the trend of dynamic data changing with time. Using the traditional model fitting can't get a good explanation for dynamic data. Therefore, many scholars developed various methods for model construction. The major drawback with most of the methods is that personal viewpoint and experience in model selection are usually influenced in them. Therefore, this paper presents a new approach on genetic-based modeling for the nonlinear time series. The research is based on the concepts of evolution theory as well as natural selection. In order to find a leading model from the nonlinear time series, we make use of the evolution rule: survival of the fittest. Through the process of genetic evolution, the AIC (Akaike information criteria) is used as the adjust function, and the membership function of the best-fitted models are calculated as performance index of chromosome. Empirical example shows that the genetic model can give an efficient explanation in analyzing Taiwan exchange rates, especially when the structure change occurs.