Although biophysical yield responses to local warming have been studied, we know little about how crop yield growth-a function of climate and technology-responds to global temperature and socioeconomic changes. Here, we present the yield growth of major crops under warming conditions from preindustrial levels as simulated by a global gridded crop model. The results revealed that global mean yields of maize and soybean will stagnate with warming even when agronomic adjustments are considered. This trend is consistent across socioeconomic assumptions. Low-income countries located at low latitudes will benefit from intensive mitigation and from associated limited warming trends (1.8 degrees C), thus preventing maize, soybean and wheat yield stagnation. Rice yields in these countries can improve under more aggressive warming trends. The yield growth of maize and soybean crops in high-income countries located at mid and high latitudes will stagnate, whereas that of rice and wheat will not. Our findings underpin the importance of ambitious climate mitigation targets for sustaining yield growth worldwide.