The Asian giant hornet (AGH, Vespa mandarinia) is the world’s largest hornet, occurring naturally in the Indomalayan region, where it is a voracious predator of pollinating insects including honey bees. In September 2019, a nest of Asian giant hornets was detected outside of Vancouver, British Columbia; multiple individuals were detected in British Columbia and Washington state in 2020; and another nest was found and eradicated in Washington state in November 2020, indicating that the AGH may have successfully wintered in North America. Because hornets tend to spread rapidly and become pests, reliable estimates of the potential invasive range of V. mandarinia in North America are needed to assess likely human and economic impacts, and to guide future eradication attempts. Here, we assess climatic suitability for AGH in North America, and suggest that, without control, this species could establish populations across the Pacific Northwest and much of eastern North America. Predicted suitable areas for AGH in North America overlap broadly with areas where honey production is highest, as well as with species-rich areas for native bumble bees and stingless bees of the genus Melipona in Mexico, highlighting the economic and environmental necessity of controlling this nascent invasion.