Western Australia's fisheries officers are hunting a rogue shark in Rottnest Island after an American tourist was mauled to death by one on Saturday.

All beaches were also closed for 24 hours to protect the public from the shark suspected of killing George Thomas Wainwright, 32, while he was diving alone 500 metres off Little Armstrong Bay. The native from Texas living in North Beach was the fourth man to be killed in a shark attack in WA's southwest coast in 14 months.

Two fisheries vessels with four crew are in Rottnest to bait the shark.

"The decision has been made that if we capture the shark we will kill it,'' said Department of Fisheries regional manager Tony Cappelluti, according to Couriermail.com.

Aside from the shark hunt ordered by Fisheries Minister Norman Moore, the first in WA's history, Premier Colin Barnett, meanwhile, is considering allowing local fishermen to catch more sharks along the state's coastline, mass shark culls and aerial patrols of the Rottnest coast.

"Culling could be considered if those sharks are staying around popular beach areas," the Courier Mail quoted Barnett as saying.

The American victim's two companions told police they were on a boat while he was diving when they noticed bubbles from the water's surface at 1:30 p.m.. Their friend's body then surfaced boring horrific injuries.

After pulling the mangled body from the water and making an emergency call, the two saw a three metre long white pointer nudge their boat.

There was a sighting of a large shark in Thomson Bay near the Rottnest ferry port minutes after the attack.

Two weeks ago, businessman Bryn Martin disappeared while swimming at Cottesloe Beach. He remains missing and authorities believed he was a victim of a shark attack.

Last month, bodyboarder Kyle Burden, 21, was killed in a shark attack near Bunker Bay.

In August 2010, surfer Nicholas Edwards, 31, was killed by a shark near Gracetown.