The projected climate change substantially impacts agricultural productivity and global food security. The cropping system models (CSM) can help estimate the effects of the changing climate on current and future crop production. The current study evaluated the impact of a projected climate change under shared socioeconomic pathways (SSPs) scenarios (SSP2-4.5 and SSP5-8.5) on the grain yield of winter wheat in the North China Plain by adopting the CSM-DSSAT CERES-Wheat model. The model was calibrated and evaluated using observed data of winter wheat experiments from 2015 to 2017 in which nitrogen fertigation was applied to various growth stages of winter wheat. Under the near-term (2021–2040), mid-term (2041–2060), and long-term (2081–2100) SSP2-4.5 and SSP5-8.5 scenarios, the future climate projections were based on five global climate models (GCMs) of the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The GCMs projected an increase in grain yield with increasing temperature and precipitation in the near-term, mid-term, and long-term projections. In the mid-term, 13% more winter wheat grain yield is predicted under 1.3 °C, and a 33 mm increase in temperature and precipitation, respectively, compared with the baseline period (1995–2014). The increasing CO2 concentration trends projected an increase in average grain yield from 4 to 6%, 4 to 14%, and 2 to 34% in the near-term, mid-term, and long-term projections, respectively, compared to the baseline. The adaptive strategies were also analyzed, including three irrigation levels (200, 260, and 320 mm), three nitrogen fertilizer rates (275, 330, and 385 kg ha−1), and four sowing times (September 13, September 23, October 3, and October 13). An adaptive strategy experiments indicated that sowing winter wheat on October 3 (traditional planting time) and applying 275 kg ha−1 nitrogen fertilizer and 260 mm irrigation water could positively affect the grain yield in the North China Plain. These findings are beneficial in decision making to adopt and implement the best management practices to mitigate future climate change impacts on wheat grain yields.