Basal conditions play an essential role in the dynamics of outlet glaciers, but direct observations at the bed of glaciers are challenging to obtain. Instead, inverse methods can be used to infer basal parameters from surface observations. Here, we use a simple ice-flow model as a forward model in an inversion scheme to retrieve the spatio-temporally variable basal stress parameter for Hagen Bræ, North Greenland, from 1990 to 2020. Hagen Bræ is a surge-type glacier with up to an order of magnitude variability of winter velocities near the grounding line. We find that downstream changes in the basal stress parameter can explain most of the variation of flow velocity, and we further identify a region of high resistance ~20–40 km from the grounding line. We hypothesise that this region of high resistance plays an important role in controlling glacier discharge.