There have been many recently proposed methods for forecasting fuzzy time series. Most of them are, however, for non-seasonal fuzzy time series. A definition of seasonal fuzzy time series was firstly given by Song (Q. Song, Seasonal forecasting in fuzzy time series, Fuzzy Sets and Systems 107 (1999), 235-236). In his paper, the model was a first order seasonal fuzzy time series. However, real time series behave very rarely in a first order seasonal fuzzy time series structure. There is a need for modeling high order seasonal structures because their structure generally is more complicated. We make a definition for a high order seasonal fuzzy time series and propose a new approach based on artificial neural networks for forecasting a high order seasonal fuzzy time series. This proposed method is applied to the time series of the international tourism demand of Turkey. The results from this approach are compared to the results obtained from conventional seasonal fuzzy time series methods. From this comparisons we observe that the new method improve the forecasting accuracy.