One of the central challenges for global food security is the growing pressure from increasingly frequent extreme weather events that results in sharp drops in crop yield and disruptions in the food supply. Such pressure can potentially be alleviated by international crop trade, which plays a crucial role in reallocating food commodities from surplus to deficit regions. However, few studies have examined the influence of extreme weather events and the synchrony of crop yield anomalies on trade linkages among nations. To investigate such influence, we used the international trade network of wheat as an example, developed relevant covariates, and tested specialized statistical and machine learning methods. The results show that countries with higher differences in extreme weather stress tend to have higher import volumes and more trade partners. Trade partnerships are more likely to be established between countries with synchronous yield variations. These findings indicate that increase in heat stress and co-occurring yield loss could lead to future higher dependence on imports, especially for vulnerable import dependent nations, and affect the stability of wheat supply. Hence, the current international trade network needs to be improved by contemplating the patterns of extreme weather and yield synchrony among countries.