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.
The animal's jaw mechanism, which shoots forward when it detects prey and then retracts under its fleshy, spade-shaped snout, fascinates McGrouther.
"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."
The latest goblin shark specimen, from which tissue samples have been taken for genetic testing, will be preserved by the museum and made available for research.