The global ionospheric response to a stratospheric sudden warming (SSW) is studied using three-dimensional electron density maps derived from radio occultation observations of FORMOSAT-3/COSMIC during the 2009 SSW periods. Results show that the ionospheric electron density at EIA crests exhibit a morning/early afternoon increase followed by an afternoon decrease and an evening increase, indicative of a semidiurnal component during the SSW period, which is consistent with recent studies. The latitude-altitude electron density slice maps show that the SSW related modifications of the equatorial plasma fountain interact with the existing summer-to-winter neutral winds and resulting in a north-south asymmetry. The global ionospheric response shows a clear longitudinal dependence in the equatorial plasma fountain enhancement during morning/early afternoon, inferred from the duration of the equatorial ionization anomaly (EIA) enhancement. Following the enhancement, prominent global EIA reductions resulting from the equatorial plasma fountain weakening in the afternoon sector are seen. The ionospheric response to the 2009 SSW event is also compared with the usual seasonal variation during January-February 2007. Instead of showing the electron density increase in the northern hemisphere and decrease in the southern hemisphere as the usual seasonal variation does, the SSW period ionosphere shows prominent global electron density reductions in the afternoon period during the 2009 SSW event.