Climate change led to increased temperature and variable rainfall, which may pose great threats to both agricultural productions and environmental impacts. In this study, we aim to explore how changing climate and its extremes in the 20th and 21st-century influence system water use efficiency (sWUE) of a corn-soybean cropping rotation in a humid sub-tropic environment, and how much can cover crops mitigate these impacts. Different from the traditional yield-focused water use efficiency (WUE), sWUE addresses both production and environmental quality goals by considering grain yields and all major system water losses (evapotranspiration, runoff, and drainage). A calibrated crop simulation model, Root Zone Water Quality Model version 2 (RZWQM2), was applied to simulate grain yields and all major system water losses. The model was forced by daily climate data from in situ observations during 1956–2015 and 10 downscaled and bias corrected General Circulation Model (GCMs) projections under the representative concentration pathways (RCP) 4.5 and 8.5 scenarios during 2020–2079. The results showed that, under the historical baseline and the future RCP4.5 and RCP8.5 scenarios, due to the growth of cover crops, the sWUE for corn were improved by 1.7%, 2.6% and 2.3%, respectively (p-value < 0.001), and for soybean by 0.7% (p = 0.06), 1.0% (p-value < 0.001) and 0.9% (p-value < 0.001). Soil evaporation, as the largest source of water loss from the cropping system, was significantly decreased by 1.7%, 2.6% and 2.3% during the corn growing season, and by 0.7%, 1.0% and 0.9% during the soybean growing season. The annual drainage was decreased by 38 mm, 53 mm and 67 mm, under the baseline, RCP4.5 and RCP8.5, respectively. With the incorporation of wheat cover crops, the correlations of temperature or precipitation extremes with grain yields and major water losses were mostly decreased, suggesting that growing cover crop is an effective means to mitigate the impact of climate extremes on sWUE of a corn-soybean cropping.