Despite global warming, total Antarctic sea ice coverage increased over 1979-2013. However, the majority of Coupled Model Intercomparison Project phase 5 models simulate a decline. Mechanisms causing this discrepancy have so far remained elusive. Here we show that weaker trends in the intensification of the Southern Hemisphere westerly wind jet simulated by the models may contribute to this disparity. During austral summer, a strengthened jet leads to increased upwelling of cooler subsurface water and strengthened equatorward transport, conducive to increased sea ice. As the majority of models underestimate summer jet trends, this cooling process is underestimated compared with observations and is insufficient to offset warming in the models. Through the sea ice-albedo feedback, models produce a high-latitude surface ocean warming and sea ice decline, contrasting the observed net cooling and sea ice increase. A realistic simulation of observed wind changes may be crucial for reproducing the recent observed sea ice increase.