The air traffic system is a complex nonlinear system with fractal characteristics. In order to more accurately grasp the spatial and temporal distribution structure of flight trajectories, and explore the application prospects of fractal methods in the field of flight trajectory mining, ADS-B data from Guangzhou Airport on October 11, 2023 was first collected, with 522 trajectories running northward as the research object. Subsequently, the improved division method was used to calculate the fractal dimension of the trajectory. Then, the multifractal spectrum of the trajectory was calculated using the detrended cross-correlation analysis method, and the multifractal characteristics of the trajectory were analyzed. Finally, through case analysis, the feasibility of applying fractal feature quantities in abnormal trajectory recognition problems was studied. The calculation results show that 99.43% of the flight trajectories in this article have fractal features, 93.68% of the flight trajectories have multifractal features, and three hovering waiting flight trajectories were identified. The research results further validate the fractal characteristics of air traffic systems and indicate that fractal methods have certain potential applications in identifying abnormal trajectories. However, the accuracy and universality of this method still need further research.