The Cook Ice Cap (CIC) on the sub-Antarctic Kerguelen Islands recently experienced extremely negative surface mass balance. Further deglaciation could have important impacts on endemic and invasive fauna and flora. To put this exceptional glacier evolution into a multi-centennial-scale context, we refined the evolution of the CIC over the last millennium, investigated the associated climate conditions and explored its potential evolution by 2100 ce. A glaciological model, constrained by cosmic ray exposure dating of moraines, historical documents and recent direct mass balance observations, was used to simulate the ice-cap extents during different phases of advance and retreat between the last millennium and 2100 ce. Cosmogenic dating suggests glacial advance around the early Little Ice Age (LIA), consistent with findings from other sub-Antarctic studies, and the rather cold and humid conditions brought about by the negative phase of the Southern Annular Mode (SAM). This study contributes to our currently limited understanding of palaeoclimate for the early LIA in the southern Indian Ocean. Glaciological modelling and observations confirm the recent decrease in CIC extent linked to the intensification of the SAM. Although affected by large uncertainties, future simulations suggest a complete disappearance of CIC by the end of the century.