In this paper, the chaotic characteristics of air traffic flow are studied, ADS-B data easily available to ground aviation users are selected as the basic data of traffic flow, and a high-dimensional prediction model of air traffic flow time series based on the non-iterative PSR-ELM algorithm is established. The prediction results of the proposed algorithm are then compared with those of the SVR algorithm, which requires iteration. Moreover, airspace operation data before and after the outbreak of the COVID-19 epidemic are selected as the experimental scene, and the prediction effects of time series with different degrees of chaos are comparatively analyzed. The experimental results reveal that the PSR-ELM algorithm achieves fast and accurate results, and, when the traffic flow state is sparse, the degree of chaos is reduced and the prediction effect is improved. The findings of this research provide a reference for air traffic flow theory.