"A British man has died during a trek across Greenland's ice sheet, the British Foreign and Commonwealth Office has said.
The FCO said the other men were recovering in hospital.
Greenland is home to the second largest icecap in world.
On a fundraising webpage before setting out, Mr Goodeve-Docker said he and his fellow travellers would be conducting the expedition unsupported across what he described as one of the most dazzling, beautiful, yet barren and deadly landscapes in the world.
A statement released by the FCO said: "We are aware that three British nationals were in difficulty during an expedition in Greenland, and have been rescued by the authorities.
"Sadly, one of the team, Philip Goodeve-Docker, died. The other two British nationals are in hospital."
It added: "We are providing consular assistance to their families at this difficult time.""