Climate change can impact the yield and water footprint of crops. Therefore, assessing such impacts carries great significance for regional water and food security. This study validated and verified the variety parameters of winter wheat for the Decision Support System for Agrotechnology Transfer (DSSAT) model, using the long-term (1993–2013) growth and yield data observed from six agricultural experiment stations in the Haihe River Basin (HRB), China. The growth process was simulated under three representative concentration pathways (RCPs), named RCP2.6, RCP4.5, and RCP8.5—climate scenarios driven by the HadGEM2-ES model. The variety parameters of winter wheat showed high accuracy in the simulation of the anthesis and maturity dates, and could be used for long-term prediction of the growth process. The trends of climate change had positive impacts on the water footprint of winter wheat but adverse impacts on the yield. The growing period was shortened by 3.6 days, 4.7 days, and 5.0 days per decade in the RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively, due to the rapid accumulation of heat. The yield would be increased in lower emissions scenarios (17% in RCP2.6), but decreased in high-emissions scenarios due to high temperatures, which may restrict the growth of wheat. The water footprint was decreased by 10%, 11%, and 13% in the RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively, indicating that the water-use efficiency could be improved in the future. The results showed broad application prospects of the DSSAT model in simulating the response of crop growth to climate change.