James Isbister caught the 6ft-long ling while fishing off Muckle Flugga on Saturday.
Mr Isbister is awaiting confirmation from the relevant authorities of its possible record-breaking status.
The fish is currently being kept in his mother's freezer. "It was a very big fight," he said.
He said he would keep trying to catch an even larger fish.
He told BBC Scotland: "Muckle Flugga is renowned for big fish.
"It took about 20 or 30 minutes.
"I knew it was a big fish but I didn't realise it was that size - I am 6ft 5in and it's as big as me."
Mr Isbister added: "It's in my mum's freezer. We had to make room for it, it fills the whole freezer.
"I am a local celebrity at the moment."
A Shetland fisherman is celebrating after reeling in a giant fish weighing more than 67lbs (30kg).