Increasing sea surface temperatures in the tropical Atlantic Ocean and measures of Atlantic hurricane activity have been reported to be strongly correlated since at least 1950 (refs 1, 2, 3, 4, 5), raising concerns that future greenhouse-gas-induced warming could lead to pronounced increases in hurricane activity. Models that explicitly simulate hurricanes are needed to study the influence of warming ocean temperatures on Atlantic hurricane activity, complementing empirical approaches. Our regional climate model of the Atlantic basin reproduces the observed rise in hurricane counts between 1980 and 2006, along with much of the interannual variability, when forced with observed sea surface temperatures and atmospheric conditions. Here we assess, in our model system, the changes in large-scale climate that are projected to occur by the end of the twenty-first century by an ensemble of global climate models, and find that Atlantic hurricane and tropical storm frequencies are reduced. At the same time, near-storm rainfall rates increase substantially. Our results do not support the notion of large increasing trends in either tropical storm or hurricane frequency driven by increases in atmospheric greenhouse-gas concentrations.