The Soil–Water–Atmosphere–Plant (SWAP) model does not have a mulching module to simulate the effect of film mulching on soil water, heat dynamics and crop growth. In this study, SWAP model parameters were selected to simulate the soil water–heat process and crop growth, taking into account the effect of film mulching on soil evaporation, temperature, and crop growth, in order to predict the influence of future climate change on crop growth and evapotranspiration (ET). A most suitable scheme for high yield and water use efficiency (WUE) was studied by an experiment conducted in the Shiyang River Basin of Northwest China during 2017 and 2018. The experiment included mulching (M1) and non-mulching (M0) under three drip irrigation treatments, including full (WF), medium (WM), low (WL) water irrigation. Results demonstrated that SWAP simulated soil water storage (SWS) well, soil temperature at various depths, leaf area index (LAI) and aboveground dry biomass (ADB) with the normalized root mean square error (NRMSE) of 16.2%, 7.5%, 16.1% and 16.4%, respectively; and yield, ET, and WUE with the mean relative error (MRE) of 10.5%, 12.4% and 14.8%, respectively, under different treatments on average. The measured and simulated results showed film mulching could increase soil temperature, promote LAI during the early growth period, and ultimately improve ADB, yield and WUE. Among the treatments, M1WM treatment with moderate water deficit and film mulching could achieve the target of more WUE, higher yield, less irrigation water. Changes in atmospheric temperature, precipitation, and CO2 concentration are of worldwide concern. Three Representative Concentration Pathway (RCP) scenarios (RCP2.6, RCP4.5, RCP8.5) showed a negative effect on LAI, ADB and yield of seed-maize. The yield of seed-maize on an average decreased by 33.2%, 13.9% under the three RCPs scenarios for film mulching and non-mulching, respectively. Predicted yields under film mulching were lower than that under non-mulching for the next 30 years demonstrating that current film mulching management might not be suitable for this area to improve crop production under the future climate scenarios.