This study forecast the tourism demand of Jeju island using the monthly time series data for the number of tourists(domestic and foreign), and compare the forecasting results and real work using two models, ARMA(or ARIMA) and GAM. The ARMA(or ARIMA) is a more popular to forecast time series data in previous studies, however we consider the non-parametric model(GAM) for adjusting nonlinear characteristics of periodic series, such as a world unobservable trend. We use a ARMA as a reference model, because the number of tourists in Jeju shows a stable time series after the unit root test. We also forecast using GAM, and compare the predictive power of the model through the RMSE value of tourist demand for 2017 in Jeju. The results show that the ARMA model has a good predictive power for forecasting the domestic demand, but the predictive power of the GAM is better when forecasting the foreign demand. And it give a important political implication about changing foreign tourism policy in a bid for Chinese tourists. Also, in terms of applying the methodology, it imply a separate consideration of the model that reflects the characteristics of each time series data.