Increasing exploration and exploitation activity in the Arctic Ocean has intensified maritime traffic in the Barents Sea. Due to the sparse population and insufficient oil spill response infrastructure on the extensive Barents Sea shoreline, it is necessary to address the possibility of offshore accidents and study hazards to the local environment and its resources. Simulations of surface oil spills were conducted in south-east of the Barents Sea to identify oil pollution trajectories. The objective of this research was to focus on one geographical location, which lies along popular maritime routes and also borders with sensitive ecological marine and terrestrial areas. As a sample of traditional heavy bunker oil, IFO-180LS (2014) was selected for the study of oil spills and used for the 30-year simulations. The second oil case was medium oil type: Volve (2006)—to give a broader picture for oil spill accident scenarios. Simulations for four annual seasons were run with the open source OpenDrift modelling tool using oceanographic and atmospheric data from the period of 1988–2018. The modelling produced a 30-year probability map, which was overlapped with environmental data of the area to discuss likely impacts to local marine ecosystems, applicable oil spill response tools and favourable shipping seasons. Based on available data regarding the environmental and socio-economic baselines of the studied region, we recommend to address potential threats to marine resources and local communities in more detail in a separate study.