Carl Spencer, is believed to have died from decompression sickness – the bends – according to the countrys merchant marine ministry.
Mr Spencer was part of a 17-member crew commissioned by the magazine to film the wreck of HMHS Britannic.
New Zealander Peter Mesley is part of the film crew.
Carl was one of the Key Note speakers at the recent OZTeK Dive Expo held in Sydney Australia 21 – 22 March.
The British World War I hospital ship, and sister ship of the Titanic, sank off the Greek Aegean island of Kea in 1916 after hitting a mine, with the loss of 30 lives.
“A Super Puma rescue helicopter was dispatched to collect the diver who was unconscious with decompression sickness symptoms,” a ministry spokeswoman said.
“He did not regain consciousness and was pronounced dead on arrival at the Athens Navy hospital.”
The National Geographic team had secured permission to film the wreck of the Britannic from May 19 to 31, she added.
No one from National Geographic was available to immediate comment.
Decompression sickness is caused by surfacing too quickly after a deep dive.
The condition can cause rashes, joint pain, headaches, and paralysis.
Death only occurs in extreme cases.
It can take hours or even days after a dive before sufferers become aware that they have decompression sickness.