The group is calling for a million signatures on a petition urging an end to oil exploration and unsustainable fishing and said celebrities such as Sir Paul McCartney and actor Robert Redford are among the effort's backers, the BBC reported Thursday.
The move comes as a response to what Greenpeace said was the "epic failure" of the Rio+20 environmental summit in Brazil aimed to put the global economy on a more sustainable footing.
Greenpeace has condemned governments at the summit, accusing them of failing to press forward on issues such as ending fossil fuel subsidies, enhancing energy efficiency and committing to the idea of a "green economy."
"The fightback starts here," Kumi Naidoo, executive director of Greenpeace International," said.
"The arctic is coming under assault, and needs people from around the world to stand up and demand action to protect it," he said. "A ban on offshore oil drilling and unsustainable fishing would be a huge victory against the forces ranged against this precious region and the four million people who live there."
Explorers, business leaders, actors and musicians are among the first signatories on the petition, Greenpeace said.
"It seems madness that we are willing to go to the ends of the earth to find the last drops of oil when our best scientific minds are telling us we need to get off fossil fuels to give our children a future," Paul McCartney said.