Facing the high possibility of future severe water resources scarcity, the Haihe River Basin in the North China Plain is an important region for climate change studies. This study employed an improved SWAT model with a Management Allowed Depletion (MAD) auto-irrigation method to assess the impacts of future climate change on water cycle and crop growth of irrigated winter wheat and summer maize in the Haihe River Basin, China. A total of 27 Global Climate Models (GCMs) from the latest Coupled Model Intercomparison Project 6 (CMIP6) and two Shared Socioeconomic Pathways (SSP2–4.5 and SSP5–8.5) were used to drive the SWAT-MAD model to simulate crop growth and water balance components for two future periods of 2041–2070 (2050s) and 2071–2100 (2080s). Data from almost all GCMs showed an increase in annual mean maximum air temperature, minimum air temperature, total precipitation, and solar radiation across the Haihe River Basin. Winter wheat yields increased by 15.6% (SSP245) and 16.3% (SSP585) by 2050s, and by 17.1% (SSP245) and 10.0% (SSP585) by 2080s, respectively. Summer maize yields increased by 8.9% (SSP245) and 9.6% (SSP585) by 2050s, and by 12.6% (SSP245) and 6.1% (SSP585) by 2080s, respectively. The change of leaf area index (LAI) indicated an advance in phenology of crops, which might be related to the increase in temperature. In the four future climate scenarios, precipitation, percolation, and surface runoff increased by 19.16–57.25 mm, 7.26–22.18 mm, and 1.45–4.87 mm during winter wheat growing season, 125.41–205.24 mm, 51.03–96.37 mm, and 33.97–68.69 mm during summer maize growing season. However, the irrigation amounts decreased by 18.82–83.74 mm and 35.71–50.92 mm during wheat and maize growing seasons, respectively. The annual Net Groundwater Use (NGU) decreased with time and the crop water productivity (CWP) increased in the future, which have positive effects on the sustainable development in this double-cropping system with intensive irrigation management.