Forecasting is the basis of planning. Previous studies on international tourism forecasting have mostly examined international tourist arrivals. Few studies discuss international travelers for specific purposes. Tourists from Western countries are the main source of tourists for leisure purpose. Economic factors generally have a significant effect on the international tourist demand. Nevertheless in different settings, there will be different conclusions. Consequently, the study supposes the recurrent neural network with genetic algorithms and the ARIMAX model to forecast numbers of tourists to Taiwan from USA, U.K, Germany, and Australia for leisure, and analyzes economic factors. The findings can help the development of the Taiwan’ tourism industry.