A popular Western Australian beach remains closed after 33-year-old Peter Kurmann was attacked and killed by a shark on Saturday morning.

Police say Mr Kurmann, from the town of Vasse, near Busselton, had anchored his boat about 1.7 kilometres off Stratham Beach and was diving for crayfish with his brother when he was attacked just after 9:00am (AWST).

The shark is believed to be a four-metre great white, and a patrol plane has spotted a similar sized shark south of the attack site, about 600 metres offshore.

Tony Cappelluti from the Department of Fisheries says a boat has gone to the area.

"We will attempt to take it. Whether we destroy it is an issue that'll be decided at the time by the relevant people able to give that order," he said.

Mr Kurmann's body was brought to shore two hours after the attack, along with the boat he and his brother had been using.

His brother, Gian, says his family has lost a son, a brother, a husband and a wonderful father.

It is the fourth fatal shark in Western Australia in seven months.

Bodyboarder Kyle Burden, 21, was killed in Bunker Bay in September, while 64-year-old Bryn Martin disappeared off Perth's Cottesloe Beach in October. It is presumed he was taken by a shark.

Less than two weeks after that, 32-year-old George Wainwright was killed by a shark off Rottnest Island.

The deaths prompted the State Government to spend millions of dollars on initiatives aimed at preventing further attacks.

Authorities say there is no evidence shark numbers are increasing.

Tina Thorne from the Government's Shark Response Unit says more research is needed.

"What we'd like to do is put some solid science behind some of those theories and prove them or disprove them," she said.