One potential impact from greenhouse-gas emissions is increasing damage from extreme events. Here, we quantify how climate change may affect tropical cyclone damage. We find that future increases in income are likely to double tropical cyclone damage even without climate change. Climate change is predicted to increase the frequency of high-intensity storms in selected ocean basins depending on the climate model. Climate change doubles economic damage, but the result depends on the parameters of the damage function. Almost all of the tropical cyclone damage from climate change tends to be concentrated in North America, East Asia and the Caribbean–Central American region. This paper provides a framework to combine atmospheric science and economics, but some effects are not yet modelled, including sea-level rise and adaptation.