The prehistoric-looking goblin sharks live on deep sea bottoms and little is known about their lives.
The museum said the body of the shark, which had died by the time it was given to the local aquarium, had nonetheless been well kept and would be an asset to its collection.
"It's pretty impressive, it's not hideous it's beautiful," said the Australian Museum's fish collection manager Mark McGrouther, who described its teeth as looking like "little daggers".
McGrouther said this was only the fourth goblin shark to be acquired by the museum in Sydney, with the first two collected in the 1980s.
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The latest was picked up by a fisherman in January. It was found near Eden, off Australia's southeast coast, at a depth of about 200 metres (656 feet) and delivered to a local aquarium which kept it in excellent condition for the museum.
McGrouther said he was "thrilled" to handle the shark, which is found in the Pacific, Atlantic and Indian oceans. The species, whose scientific name is "Mitsukurina owstoni", is thought to be a living fossil dating back some 125 million years.
"I suspect because it has got soft, flabby musculature, it doesn't need much energy... So it will swim slowly over the bottom just using its snout like a metal detector," he told AFP.
"It will be sweeping over the bottom and when it detects a small fish, or a crab or a squid it will shoot those jaws out 'wham' and capture whatever it is.
"It will spear it with those sharp pointed teeth and then just wolf it down whole."