Fully coupled ice-sheet-climate modelling over 10 000-100 000-year timescales at high spatial and temporal resolution remains beyond the capability of current computational systems. Forcing an ice-sheet model with precalculated output from a general circulation model (GCM) offers a middle ground, balancing the need to accurately capture both long-term processes, in particular circulation-driven changes in precipitation, and processes requiring a high spatial resolution like ablation. Here, we present and evaluate a model set-up that forces the ANICE 3-D thermodynamic ice-sheet-shelf model calculating the four large continental ice sheets (Antarctica, Greenland, North America, and Eurasia) with precalculated output from two steady-state simulations with the HadCM3 (GCM) using a so-called matrix method of coupling both components, whereby simulations with various levels of pCO2 and ice-sheet configuration are combined to form a time-continuous transient climate forcing consistent with the modelled ice sheets. We address the difficulties in downscaling low-resolution GCM output to the higher-resolution grid of an ice-sheet model and account for differences between GCM and ice-sheet model surface topography ranging from interglacial to glacial conditions. Although the approach presented here can be applied to a matrix with any number of GCM snapshots, we limited our experiments to a matrix of only two snapshots. As a benchmark experiment to assess the validity of this model set-up, we perform a simulation of the entire last glacial cycle from 120 kyr ago to present day. The simulated eustatic sea-level drop at the Last Glacial Maximum (LGM) for the combined Antarctic, Greenland, Eurasian, and North American ice sheets amounts to 100 m, in line with many other studies. The simulated ice sheets at the LGM agree well with the ICE-5G reconstruction and the more recent DATED-1 reconstruction in terms of total volume and geographical location of the ice sheets. Moreover, modelled benthic oxygen isotope abundance and the relative contributions from global ice volume and deep-water temperature agree well with available data, as do surface temperature histories for the Greenland and Antarctic ice sheets. This model strategy can be used to create time-continuous ice-sheet distribution and sea-level reconstructions for geological periods up to several million years in duration, capturing climate-model-driven variations in the mass balance of the ice sheet.