Spatial and temporal variabilities of Kelvin waves during stratospheric sudden warming (SSW) events are investigated by the ERA-Interim reanalysis data, and the results are validated by the COSMIC temperature data. A case study on an exceptionally large SSW event in 2009, and a composite analysis comprising 18 events from 1980 to 2013 are presented. During SSW events, the average temperature increases by 20 K in the polar stratosphere, while the temperature in the tropical stratosphere decreases by about 4 K. Kelvin wave with wave numbers 1 and 2, and periods 10–20 days, clearly appear around the tropical tropopause layer (TTL) during SSWs. The Kelvin wave activity shows obvious coupling with the convection localized in the India Ocean and western Pacific (Indo-Pacific) region. Detailed analysis suggests that the enhanced meridional circulation driven by the extratropical planetary wave forcing during SSW events leads to tropical upwelling, which further produces temperature decrease in the tropical stratosphere. The tropical upwelling and cooling consequently result in enhancement of convection in the equatorial region, which excites the strong Kelvin wave activity. In addition, we investigated the Kelvin wave acceleration to the eastward zonal wind anomalies in the equatorial stratosphere during SSW events. The composite analysis shows that the proportion of Kelvin wave contribution ranges from 5 to 35 % during SSWs, much larger than in the non-SSW mid-winters (less than 5 % in the stratosphere). However, the Kelvin wave alone is insufficient to drive the equatorial eastward zonal wind anomalies during the SSW events, which suggests that the effects of other types of equatorial waves may not be neglected.