Over the past decade, ice loss from the Greenland Ice Sheet increased as a result of both increased surface melting and ice discharge to the ocean1,2. The latter is controlled by the acceleration of ice flow and subsequent thinning of fast-flowing marine-terminating outlet glaciers3. Quantifying the future dynamic contribution of such glaciers to sea-level rise (SLR) remains a major challenge because outlet glacier dynamics are poorly understood4. Here we present a glacier flow model that includes a fully dynamic treatment of marine termini. We use this model to simulate behaviour of four major marine-terminating outlet glaciers, which collectively drain about 22 per cent of the Greenland Ice Sheet. Using atmospheric and oceanic forcing from a mid-range future warming scenario that predicts warming by 2.8 degrees Celsius by 2100, we project a contribution of 19 to 30 millimetres to SLR from these glaciers by 2200. This contribution is largely (80 per cent) dynamic in origin and is caused by several episodic retreats past overdeepenings in outlet glacier troughs. After initial increases, however, dynamic losses from these four outlets remain relatively constant and contribute to SLR individually at rates of about 0.01 to 0.06 millimetres per year. These rates correspond to ice fluxes that are less than twice those of the late 1990s, well below previous upper bounds5. For a more extreme future warming scenario (warming by 4.5 degrees Celsius by 2100), the projected losses increase by more than 50 per cent, producing a cumulative SLR of 29 to 49 millimetres by 2200.