The El Nino/Southern Oscillation is Earth's most prominent source of interannual climate variability, alternating irregularly between El Nino and La Nina, and resulting in global disruption of weather patterns, ecosystems, fisheries and agriculture(1-5). The 1998-1999 extreme La Nina event that followed the 1997-1998 extreme El Nino event(6) switched extreme El Nino-induced severe droughts to devastating floods in western Pacific countries, and vice versa in the southwestern United States(4,7). During extreme La Nina events, cold sea surface conditions develop in the central Pacific(8,9), creating an enhanced temperature gradient from the Maritime continent to the central Pacific. Recent studies have revealed robust changes in El Nino characteristics in response to simulated future greenhouse warming(10-12), but how La Nina will change remains unclear. Here we present climate modelling evidence, from simulations conducted for the Coupled Model Intercomparison Project phase 5 (ref. 13), for a near doubling in the frequency of future extreme La Nina events, from one in every 23 years to one in every 13 years. This occurs because projected faster mean warming of the Maritime continent than the central Pacific, enhanced upper ocean vertical temperature gradients, and increased frequency of extreme El Nino events are conducive to development of the extreme La Nina events. Approximately 75% of the increase occurs in years following extreme El Nino events, thus projecting more frequent swings between opposite extremes from one year to the next.