When a hurricane strikes land, the destruction of property and the environment and the loss of life are largely confined to a narrow coastal area. This is because hurricanes are fuelled by moisture from the ocean1-3, and so hurricane intensity decays rapidly after striking land4,5. In contrast to the effect of a warming climate on hurricane intensification, many aspects of which are fairly well understood6-10, little is known of its effect on hurricane decay. Here we analyse intensity data for North Atlantic landfalling hurricanes11 over the past 50 years and show that hurricane decay has slowed, and that the slowdown in the decay over time is in direct proportion to a contemporaneous rise in the sea surface temperature12. Thus, whereas in the late 1960s a typical hurricane lost about 75 per cent of its intensity in the first day past landfall, now the corresponding decay is only about 50 per cent. We also show, using computational simulations, that warmer sea surface temperatures induce a slower decay by increasing the stock of moisture that a hurricane carries as it hits land. This stored moisture constitutes a source of heat that is not considered in theoretical models of decay13-15. Additionally, we show that climate-modulated changes in hurricane tracks16,17 contribute to the increasingly slow decay. Our findings suggest that as the world continues to warm, the destructive power of hurricanes will extend progressively farther inland.