The unbelievable video was taken using an underwater camera by divers on a kayaking excursion to St Kilda in the Outer Hebrides.
During the footage, one woman is seen swimming up to the eight-metre long shark as it circled the waters off the coast of Hirta - the largest island in the St Kilda island chain.
The shark was spotted from the deck of a chartered tall ship the holidaymakers were aboard the Lady of Avenel, on July 11, and lingered in the area for four hours.
Chris Denehy is the owner of Clearwater Paddling, based on the Isle of Barra, the Outer Hebrides, and runs the kayaking excursions.
The 56-year-old said: “We go out on a tall ship to kayak around there often. Somebody spotted a basking shark about 50 metres from the ship.
“The water was so calm and the shark was swimming around close by for three or four hours.
“There were four people who went along to see it up close. Two swam across and another two rowed out in a dinghy.
“We kayak out at St Kilda a lot and we’ve often kayaked close by basking sharks but none of us have swam alongside one before.
“It’s absolutely amazing when you see it from above on the kayak but when you’re up close it’s completely different.
“It must’ve been seven or eight metres long, it was definitely an adult shark. I went out with one of the guests after Ben and his sister.
“Basking sharks have been few and far between the past couple years, but this year they’ve been more prominent.”
Basking sharks are the second largest shark in the world after the whale shark and feed in the coastal waters of the Inner and Outer Hebrides.