This study presents the results of a 2D numerical basin and petroleum systems model of the Olga Basin in the NW Barents Sea offshore northern Norway, a frontier exploration area in which there are abundant seafloor oil and gas seepages. The effects of Pleistocene ice sheet advances on rock properties and subsurface fluid migration in this area, and on seafloor hydrocarbon seepage, are not well understood. The 2D numerical model takes account of recurrent ice advances and retreats, together with related erosional and temperature effects, and investigates the influence of these parameters on fluid migration. Model results show that Pleistocene glaciations reduced the temperature in the sedimentary succession in the Olga Basin by up to 20 °C, for example in the uppermost Cretaceous and Jurassic sediments which underlie the seafloor down to a depth of 0.5 to 1 km. The decrease in temperature was in general predominantly related to the intensity of glacial erosion, which was set in this study to a depth of 600 m based on previous studies. Hydrocarbon fluids expelled from potential thermogenic source rocks of Carboniferous to Triassic ages on the SW margin of the Olga Basin migrated to the seafloor through permeable carrier beds. However, fluid migration to the surface in the NE of the study area took place along fault conduits. In a closed fault model scenario, only 0.3 Mt of hydrocarbons are modelled to have migrated along the 0.5 km wide model section; in a second scenario with partially open faults, about 22 Mt of hydrocarbons, representing about 11% of the total hydrocarbons generated by potential thermogenic source rocks in the study area, were lost to the surface during the Pleistocene. The potential for microbial methane generation in the Olga Basin was limited both during the Pleistocene and at the present day due to the significant reduction in temperature during glacial episodes, and due to the intense glacial‐related erosion of the Mesozoic to Cenozoic stratigraphy. During glacial stages, the gas hydrate stability zone beneath the ice sheet is modelled to have extended to a depth of up to 900 m for a pure methane composition, and to a depth of up to 1100 m for a possible thermogenic‐sourced mixed gas composition of 90% methane, 7% propane and 3% ethane. Gas hydrates with this mixed composition are modelled to have been stable in the Olga Basin during the last three glacial advances and into the present. These modelling results provide an insight into the key factors controlling the migration and surface leakage of hydrocarbon fluids in the Olga Basin region, and into the effects of glaciations on rock properties in a glaciated basin.