Forecasting is an activity to estimate what will happen in the future, one method that can be used is Exponential Smoothing. In this study used the smoothing method of Exponential Smoothing Holt-Winters Additive with three parameters that can be used for prediction of time series data that has trend patterns and seasonal patterns. The problem that arises in this method is to determine the optimum parameter to minimize the forecast error value. This study uses the Golden Section optimization method to estimate the optimum parameters that minimize the MAPE value. The data used is data on foreign tourists who use accommodation services in Yogyakarta from the period January 2009 to December 2016 that have trend patterns and additive seasonal patterns. In simplifying the optimization calculation process, a syntax using RStudio is arranged which contains the Golden Section algorithm to determine the combination that has the optimum parameters. In this optimization there are two treshold error, namely 0.001 and 0.00001. The results showed that the parameter estimator with the Golden Section method for the treshold error of 0.001 obtained MAPE of 18,96732% and for treshold error of 0.00001 MAPE was 18,96536%. This value is in the same MAPE criteria which is 10% ─ 20% (good) so that the selection of the best model is determined based on minimal iteration. Therefore the weighting parameter value used is the result of optimization with ε ≤ 0.001, then from the selected model it is used to predict the number of foreign tourists using accommodation services in Yogyakarta in the next 12 months.