With the fast growth of the international tourism industry, it has been a challenge to forecast the tourism demand in the international tourism market. Traditional forecasting methods usually suffer from the prediction accuracy problem due to the high volatility, irregular movements and non-stationarity of the tourist time series. In this study, a novel single dendritic neuron model (SDNM) is proposed to perform the tourism demand forecasting. First, we use a phase space reconstruction to analyze the characteristics of the tourism and reconstruct the time series into proper phase space points. Then, the maximum Lyapunov exponent is employed to identify the chaotic properties of time series which is used to determine the limit of prediction. Finally, we use SDNM to make a short-term prediction. Experimental results of the forecasting of the monthly foreign tourist arrivals to Japan indicate that the proposed SDNM is more efficient and accurate than other neural networks including the multi-layered perceptron, the neuro-fuzzy inference system, the Elman network, and the single multiplicative neuron model.