Robinia pseudoacacia has been widely planted on the Chinese Loess Plateau for soil and water conservation. Declining growth of R. pseudoacacia plantations has become a recently emerging challenge for revegetation and sustainable forest management in this region. In the suitable area of R. pseudoacacia, we selected four representative study sites along a precipitation gradient (aridity indexes of 1.3 at Fufeng, 1.5 at Changwu, 1.9 at Ansai, and 2.4 at Mizhi) and used an integrated Biome BioGeochemistry-plant hydraulic traits model (BBGC-SPERRY) to assess the climate change impacts on net primary productivity (NPP), maximum leaf area index (LAImax), actual evapotranspiration (AET), and annual average percentage loss of whole-plant hydraulic conductance (APLK) for R. pseudoacacia. We adopted climate scenario data derived from five downscaled Global Circulation Models under three Representative Concentration Pathways (RCPs2.6, RCP4.5 and RCP8.5) and set baseline (1981–2020), near future (2021–2060, NFP) and far future (2061–2099, FFP) periods. Our projections show annual precipitation will significantly increase during the NFP and FFP at the Ansai and Mizhi sites and increase slightly at the Fufeng and Changwu sites during the FFP; annual maximum and minimum temperatures will increase under all RCPs. The mean NPP and LAImax of R. pseudoacacia will significantly decrease by 9.9% (RCP4.5) to 49.1% (RCP2.6) during the NFP and by 7.4% (RCP4.5) to 50.1% (RCP2.6) during the FFP at the Changwu, Ansai, and Mizhi sites; however, both measures will significantly increase during the NFP and FFP at the Fufeng site. The AET will significantly increase during the NFP and FFP at all sites. The maximum APLK will increase from south to north along the precipitation gradient, with values greater than 60% at the Changwu, Ansai, and Mizhi sites during the NFP and FFP. These results indicate the drought-induced mortality risk of R. pseudoacacia will increase under future climate change.