"Some of the divers came so close to the female shark in the waters off Hawaii that they were able to touch it.
The shark, nearly 20ft (6m) long and weighing an estimated 2.5 tonnes, is believed to be one tagged by researchers about 20 years ago called Deep Blue.
It was attracted to the area off Oahu's south shore by the carcass of a dead sperm whale.
One of the divers, Ocean Ramsey, told the Honolulu Star Advertiser that they had been filming tiger sharks feeding on the whale when the shark arrived.
"We saw a few tigers and then she came up and all the other sharks split, and she started brushing up against the boat," she said.
"She was just this big beautiful gentle giant wanting to use our boat as a scratching post."