The environmental group said 14 of its activists scaled the West Alpha rig in Norway to protest plans to explore for oil in the Kara Sea alongside its joint venture partners Rosneft, a Russian oil company.
"ExxonMobil plans to drill in the most extreme and remote area of the arctic this year," Greenpeace campaigner Erlend Tellnes said in a statement. "This is madness."
Russian President Vladimir Putin in December signed an amnesty measure for 28 Greenpeace activists and two freelance journalists, dubbed the Arctic 30. In late 2013, the protestors scaled Gazprom's Prirazlomnaya rig, which was deployed to the arctic the previous year.
Greenpeace said it was concerned about the potential for an oil spill in the harsh arctic environment. Greenpeace said Monday it was calling for a ban on offshore drilling in the arctic.
There was no statement from Exxon or Rosneft on the protest action.
Exxon Mobil and Rosneft in 2012 agreed to develop parts of the Black Sea and the South Kara Sea in the Russian arctic. There may be as much as 85 billion barrels of oil in the area.
The Exxon Valdez struck ground off the coast of Alaska on March 24, 1989, spilling at least 260,000 barrels of oil.