The Scandinavian topography and bathymetry have been shaped by ice through numerous glacial cycles in the Quaternary. In this study, we investigate how the changing morphology has influenced the Scandinavian ice sheet (SIS) in return. We use a higher-order ice-sheet model to simulate the SIS through a glacial period on three different topographies, representing different stages of glacial landscape evolution in the Quaternary. By forcing the three experiments with the same climate conditions, we isolate the effects of a changing landscape morphology on the evolution and dynamics of the ice sheet. We find that early Quaternary glaciations in Scandinavia were limited in extent and volume by the pre-glacial bathymetry until glacial deposits filled depressions in the North Sea and built out the Norwegian shelf. From middle–late Quaternary (∼0.5 Ma) the bathymetry was sufficiently filled to allow for a faster southward expansion of the ice sheet causing a relative increase in ice-sheet volume and extent. Furthermore, we show that the formation of The Norwegian Channel during recent glacial periods restricted southward ice-sheet expansion, only allowing for the ice sheet to advance into the southern North Sea close to glacial maxima. Finally, our experiments indicate that different stretches of The Norwegian Channel may have formed in distinct stages during glacial periods since ∼0.5 Ma. These results highlight the importance of accounting for changes in landscape morphology through time when inferring ice-sheet history from ice-volume proxies and when interpreting climate variability from past ice-sheet extents.