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Countries’ reliance on global food trade networks implies that regionally different climate change impacts on crop yields will be transmitted across borders. This redistribution constitutes a significant challenge for climate adaptation planning and may affect how countries engage in cooperative action. This paper investigates the long-term (2070–2099) potential impacts of climate change on global food trade networks of three key crops: wheat, rice and maize. We propose a simple network model to project how climate change impacts on crop yields may be translated into changes in trade. Combining trade and climate impact data, our analysis proceeds in three steps. First, we use network community detection to analyse how the concentration of global production in present-day trade communities may become disrupted with climate change impacts. Second, we study how countries may change their network position following climate change impacts. Third, we study the total climate-induced change in production plus import within trade communities. Results indicate that the stability of food trade network structures compared to today differs between crops, and that countries’ maize trade is least stable under climate change impacts. Results also project that threats to global food security may depend on production change in a few major global producers, and whether trade communities can balance production and import loss in some vulnerable countries. Overall, our model contributes a baseline analysis of cross-border climate impacts on food trade networks.