The anticipated retreat of glaciers around the globe will pose far-reaching challenges to the management of fresh water resources and significantly contribute to sea-level rise within the coming decades. Here, we present a new model for calculating the 21st century mass changes of all glaciers on Earth outside the ice sheets. The Global Glacier Evolution Model (GloGEM) includes mass loss due to frontal ablation at marine-terminating glacier fronts and accounts for glacier advance/retreat and surface Elevation changes. Simulations are driven with monthly near-surface air temperature and precipitation from 14 Global Circulation Models forced by the RCP2.6, RCP4.5 and RCP8.5 emission scenarios. Depending on the scenario, the model yields a global glacier volume loss of 25-48% between 2010 and 2100. For calculating glacier contribution to sea-level rise, we account for ice located below sea-level presently displacing ocean water. This effect reduces glacier contribution by 11-14%, so that our model predicts a sea-level equivalent (multi-model mean +-1 standard deviation) of 79+-24 mm (RCP2.6), 108+-28 mm (RCP4.5) and 157+-31 mm (RCP8.5). Mass losses by frontal ablation account for 10% of total ablation globally, and up to 30% regionally. Regional equilibrium line altitudes are projected to rise by 100-800 m until 2100, but the effect on ice wastage depends on initial glacier hypsometries.