Compound events of climate extremes such as extremely high temperature and low precipitation during crop growing seasons can greatly affect agricultural production and food security. No study has investigated how Compound Extreme Hot and Dry days (CEHD days) during crop-growing seasons have changed or will change in response to climate warming. Based on observations, we find upward trends in CEHD days during wheat and maize growing seasons in China in the historical period 1980-2015. These trends are remarkably different during wheat and maize growing seasons, pointing to the need for targeted analysis focusing on crop-specific growing seasons. Projections of future temperature and precipitation from the Coordinated Regional Climate Downscaling Experiment show that upward trends will continue into future. On average over China, the frequencies of CEHD days during wheat and maize growing seasons are projected to increase respectively by 168% and 162% in 2036-2050 relatively to 1980-2015 under the RCP8.5 emissions scenario. The projected increases may have serious implications for China's food production, adding to the need for resilience planning to limit the impacts of growing-season CEHD days.