Sudden stratospheric warming (SSW) events occurred in winter polar stratosphere play a significant effect on the global ionosphere and atmosphere. However, the SSW-induced effects on small-scale structure in the ionosphere are generally lack of understanding. Ionospheric F-layer irregularities is kind of small-scale structure, which can affect the trans-ionospheric radio wave, leading to so-called ionospheric scintillation phenomenon. Thus, the role of SSW on the small-scale structure in the ionosphere can be reflected by studying the characteristics of ionospheric scintillation during SSW events. In the present work, we investigate the variation of the equatorial premidnight F-layer scintillation using COSMIC/FORMOSAT-3 data during SSW events. It found that the occurrence frequency and altitude of ionospheric F-layer scintillation obviously suppressed during SSW events. It suggested that the SSW event has a significant effect on the small-scale structure in the Earth's ionosphere, having potential application for satellite navigation and communication.