The purpose of this study is to anticipate the air travel demands over the period of 164 months, from January 1997 to August 2010 using ARIMA-Intervention modeling on the selected sample data. The sample data is composed of the number of the passengers who in the domestic route for Jeju route. In the analysis work of this study, the past events which are assumed to have affected the demands for the air travel routes to Jeju in different periods were used as the intervention variables. The impacts of such variables were reflected in the presupposed demand. The intervention variables used in this study are, respectively, the World Cup event in 2002 (from May to June), 2003 SARS outbreak (from April to May), Tsunami in January 2005, and the influenza outbreak from October to December 2009. The result of the above mentioned analysis revealed that the negative intervention events, like a global outbreak of an epidemic did have negative impact on the air travel demands in a risk aversion by the users of the aviation services. However, in case of the negative intervention events in limited area, where there are possible substituting destinations for the tourists, the impact was positive in terms of the air travel demands for substituting destinations due to the rational expectation of the users as they searched for other options. Also in this study, it was discovered that there is not a binding correlation between a nation wide mega-event, such as the World Cup games in 2002, and the increased air travel demands over a short-term period.