Geoengineering by stratospheric sulfate aerosol injection may help preserve mountain glaciers by reducing summer temperatures. We examine this hypothesis for the glaciers in high-mountain Asia using a glacier mass balance model driven by climate simulations from the Geoengineering Model Intercomparison Project (GeoMIP). The G3 and G4 schemes specify use of stratospheric sulfate aerosols to reduce the radiative forcing under the Representative Concentration Pathway (RCP) 4.5 scenario for the 50 years between 2020 and 2069, and for a further 20 years after termination of geoengineering. We estimate and compare glacier volume loss for every glacier in the region using a glacier model based on surface mass balance parameterization under climate projections from three Earth system models under G3, five models under G4, and six models under RCP4.5 and RCP8.5. The ensemble projections suggest that glacier shrinkage over the period 2010-2069 is equivalent to sea-level rise of 9.0±1.6mm (G3), 9.8±4.3mm (G4), 15.5±2.3mm (RCP4.5), and 18.5±1.7mm (RCP8.5). Although G3 keeps the average temperature from increasing in the geoengineering period, G3 only slows glacier shrinkage by about 50% relative to losses from RCP8.5. Approximately 72% of glaciated area remains at 2069 under G3, as compared with about 30% for RCP8.5. The widely reported reduction in mean precipitation expected for solar geoengineering is unlikely to be as important as the temperature-driven shift from solid to liquid precipitation for forcing Himalayan glacier change. The termination of geoengineering at 2069 under G3 leads to temperature rise of about 1.3°C over the period 2070-2089 relative to the period 2050-2069 and corresponding increase in annual mean glacier volume loss rate from 0.17 to 1.1%yr-1, which is higher than the 0.66%yr-1 under RCP8.5 during 2070-2089.