Using transient climate forcing based on simulations from the Alfred Wegener Institute Earth System Model (AWI-ESM), we simulate the evolution of the Greenland Ice Sheet (GrIS) from the last interglacial (125 ka, kiloyear before present) to 2100 AD with the Parallel Ice Sheet Model (PISM). The impact of paleoclimate, especially Holocene climate, on the present and future evolution of the GrIS is explored. Our simulations of the past show close agreement with reconstructions with respect to the recent timing of the peaks in ice volume and the climate of Greenland. The maximum and minimum ice volume at around 18–17 ka and 6–5 ka lag the respective extremes in climate by several thousand years, implying that the ice volume response of the GrIS strongly lags climatic changes. Given that Greenland’s climate was getting colder from the Holocene Thermal Maximum (i.e., 8 ka) to the Pre-Industrial era, our simulation implies that the GrIS experienced growth from the mid-Holocene to the industrial era. Due to this background trend, the GrIS still gains mass until the second half of the 20th century, even though anthropogenic warming begins around 1850 AD. This is also in agreement with observational evidence showing mass loss of the GrIS does not begin earlier than the late 20th century. Our results highlight that the present evolution of the GrIS is not only controlled by the recent climate changes, but is also affected by paleoclimate, especially the relatively warm Holocene climate. We propose that the GrIS was not in equilibrium throughout the entire Holocene and that the slow response to Holocene climate needs to be represented in ice sheet simulations in order to predict ice mass loss, and therefore sea level rise, accurately.