Globalization has resulted in increases in air transportation demand and air passenger traffic. With the increases in air traffic, airports face challenges related to infrastructure, air services, and future development. Air traffic forecasting is essential to ensuring appropriate investment in airports. In this study, we combined fuzzy theory with support vector regression (SVR) to develop a fuzzy SVR (FSVR) model for forecasting international airport traffic. This model was used to predict the air traffic volumes at the world’s 10 busiest airports in terms of air traffic in 2018. The predictions were made for the period from August 2014 to December 2019. For fuzzy time series, the developed FSVR model can consider historical air traffic changes. The FSVR model can suitably divide air traffic changes into appropriate fuzzy sets, generate membership function values, and establish fuzzy relations to produce fuzzy interpolated values with minimal errors. Thus, in the prediction of continuous data, the fuzzy data with the smallest errors can be subjected to SVR to find the optimal hyperplane model with the minimum distance to the appropriate support vector sample points. The performance of the proposed model was compared with those of five other models. Of the compared models, the FSVR model exhibited the lowest mean absolute percentage error (MAPE), mean absolute error, and root mean square error for all types of traffic at all of the airports analyzed; all of the MAPE values were below 2.5. The FSVR model can predict future growth trends in air traffic, air passenger flows, aircraft flows, and logistics. An airport authority can use this model to analyze the existing operational facilities and service capacity, find bottlenecks in airport operations, and create a blueprint for future development. The findings revealed that implementing a hybrid modeling approach, specifically the FSVR model, can significantly enhance the performance of the SVR model. The FSVR model allows airlines to predict traffic growth patterns, identify viable new destinations, optimize their schedules or fleet, make accurate marketing decisions, and plan traffic effectively. The FSVR model can guide the timely construction of appropriate airport facilities with accurate predictions. Rapid, cost-effective, efficient, and balanced transportation planning enables the provision of fast, cost-effective, comfortable, safe, and convenient passenger and cargo services while ensuring the proper planning of the airport’s capacity for land-side transportation connections.