She was seen feeding on a decomposing sperm whale off Oahu island, Hawaii.
The shark in the video is believed to "Deep Blue", which is almost 20 feet long.
Ramsey previously swam with Deep Blue on research trips to Guadalupe Island, Mexico.
One of the team, who was pictured touching the enormous shark, wrote: "I am without words and at the same time I think I never stop speaking up for sharks, I am grateful beyond measure for my experiences and what they have taught me".More news: Prince Philip Involved in Car Crash Near Sandringham
"I hope my conservation images like this help people to question their perceptions and realise the beauty, and importance of sharks and I hope that they inspire the kind of compassion and connection we need to have with nature and sharks, to help protect them and co-exit alongside them", he wrote in the caption.
Ms Ramsey also told the paper: "She looks like she may be pregnant: She's shockingly wide".
Hawaii waters are usually too warm for great whites compared with California's Pacific coast, where they feed on sea lions and elephant seals, Ramsey said.
The predator was identified as "Deep Blue", who is around 50 years old, because of a tag placed on it by scientists during an appearance over 20 years ago off the coast of Mexico.More news: Senate Republicans block attempt to keep sanctions on Russian oligarch’s firms
She said: "She's probably the most gentle great white I've ever seen".
Deep Blue became an icon several years ago during Shark Week on the Discovery Channel, through her remarkable size and age.
She is unlikely to grow any more, but "she's quite large from the photos I have seen, so she has either over-gorged herself on sperm whale or she's pregnant", Ms Nasby-Lucas said. When we entered the water we had to wait because there was nothing to see. "Deep Blue has never been measured, so how could anyone make that statement?" We realised nearly immediately that she was very big. "[Jeffries] was first to spot her on 13 January 2019, and we confirmed the ID with the white shark authority, SharkPix.com this morning", he posted to Facebook. It's believed to be 6.5 metres long. The whole team felt safe. "We went out at sunrise, and she stayed with us pretty much throughout the day", she added.
George Burgess, director emeritus of the International Shark Attack File at Florida Museum of Natural History, told ABC News: 'It's a very big white shark, obviously. She's a big girl'.More news: Brexit: UK PM May survives confidence vote
"We don't want anyone to get hurt if a shark swimming around the carcass mistakes them as food".
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