The 14 stone, 7ft long shark is believed to be a porbeagle, which is found in UK waters, usually at least 10 miles off the coast.
Rich Cope, 38, who runs the Whitby-based boat charters, Mistress Sea Angling said: "It was like trying to control a car on a fishing rod! We were about 20 miles off the Whitby coast. We see them in the summer some seasons, but we don't see many. This last month there have been a couple of sightings in that area. We had only been fishing about 15 minutes when we got it on.
"We knew it was a shark, it was very exciting. I don't suppose many people have a job like mine, I love fishing and get a lot of excitement."
When asked how difficult it is to reel in a shark of that size he added: "I've never done it, I enjoy watching!"
The group managed to get the shark on board for some pictures and a quick measurement before releasing it back into the sea.
It was measured at 91 inches in length and 42 inches around its gut, giving an approximate weight of 14 stone. Rich insists even bigger ones have been caught on his boat in the past, including one weighing around 300lbs!
Peter Fearon, from Peterborough, who landed the catch while on the Whitby fishing vessel said: “Honestly, it was like being hooked into a car. It was stripping line whilst I just held on. I dug my feet in on the well gritted deck and it still dragged me around like I was being taken for a walk.
"It was tiring, my friend took over the last half of the fight, even with me lifting the rod for him, by the end of it he had to sit down for an hour. He couldn't fish he was so tired.
"My biggest catch before this was a 22lbs carp so having 200lbs of muscle and teeth on the end of the rod is something I could only imagine.
"Every minute that passed felt like 10 against the immense strength of him. My left bicep still aches today, it was better than any gym session! After I put him back in I just sat down awestruck that we just had a shark on the boat."
Porbeagle sharks can be up to 12ft long in length and are members of the same family as great white sharks and look similar in appearance.
They are normally found at least 10 miles out to sea, but have been known to drift closer to UK shores when food is scarce in deeper waters.
They are shy creatures and not known for attacking humans, with no recorded cases of a porbeagle killing a person.