Juha Aromaa, a spokesman for the environmental group, says 15 activists boarded a rig operated by the Norwegian energy company Statoil 175 kilometres off the Bear Island nature reserve early Tuesday without encountering any resistance from the crew.
Statoil was given the green light to drill in the northern part of the Barents Sea late Monday.
The rig had been on a government-ordered hiatus pending a complaint from Greenpeace.
Also, the group said 30 activists in the Dutch port of Ijmuiden on Tuesday boarded a rig contracted by Russia's Gazprom to drill in the Pechora Sea.
Greenpeace said they were removed after five hours.