HMS Hood was hit by a shell from the German battleship Bismarck in the Denmark Strait on 24 May 1941.
Only three of its 1,418 crew survived, making it the worst loss of life from a single British warship.
Dundee's Frigate Unicorn is hosting the exhibition.
It features a nine-foot model of HMS Hood along with contemporary press articles of the sinking.
Duncan Knox from Montrose, whose 18-year-old brother John was lost with the Hood, said the exhibition brought back "sad memories" of the day.
Mr Knox, 92, said: "I was walking along the docks in Montrose and a small patrol of ships went out at that time.
"The bloke said he heard on the radio that the Hood had sunk.
"When I said my brother was on it, he said 'well we hear all things''".
"It wasn't until night that it was official it had been sunk.
"John was full of life and the best friend that I ever had. His memory is always there."
Wilma Barclay from Dundee, whose cousin George Jack was lost with the Hood, said: "I can remember sadness and tears.
"What I remember was what I overheard. I knew that the ship had sunk."
HMS Hood was struck near its ammunition magazines which subsequently exploded.
The sinking took place during a huge Royal Navy pursuit of the Bismarck, which was destroyed three days later. The German death toll was more than 2,000.
A number of commemorative events are taking place on the 75th anniversary of the disaster, including the unveiling in Portsmouth of the Hood's bell, which was recently recovered from the debris field around the wreck.
Relatives of those lost on HMS Hood attended a new exhibition in Dundee on the 75th anniversary of the sinking of the Royal Navy battlecruiser.