This paper examines the dynamics for evaluating different forecasting methods for international air passenger demand in Nigeria. It achieved the objectives by forecasting international air passenger demand in the year 2018 using two single moving average, four single moving average and six single moving average; the same forecast was also achieved by using simple exponential smoothing, with smoothing constants of 0.7, 0.8, and 0.9 respectively. The most appropriate forecasting method was determined by comparing all the single moving averages with exponential smoothing. This study is very essential to airport management, airline management, concessionaires of aeronautical and non-aeronautical services, third-parties, government agencies and ministries, economic regulators, transport policy analysts and planners, and other concerned agencies, for accurate planning which affect the overall operations of international air transport movement and help to prevent problems of having excess air transport demand over air transport supply or having excess air transport supply over demand particularly in the international level. The data involved for this study was between the periods of year 2001 to year 2017, meanwhile single moving average and simple exponential smoothing were the quantitative forecasting methods adopted for forecasting, the two forecasting methods were compared using Mean Squared Deviation (MSD). It was revealed that the MSD of exponential smoothing with constant 0.8 appears to give the best year 2018 forecast as it has a lower MSD when compared to the MSD of the other forecasts.