A world champion paddleboarder who rescued a woman after she was attacked by a great white at Coogee on Saturday says it was one of the biggest sharks he's seen.

Ironman Charlie Verco is being branded a hero after he paddled towards the attack to grab the 35-year-old woman and bring her to safety.

The swimmer suffered serious arm and leg injuries at Coogee Beach in Sydney's eastern suburbs just before 11.15am on Saturday.

Witnesses told the Daily Telegraph the shark was the 'the size of a car' and Mr Verco backed up those claims after seeing the woman in the shark's jaws while nearby on his paddleboard.

'It actually grabbed one of the girls and started dragging her around a little bit. it was such an aggressive thing to watch happen,' Mr Verco told Nine News.

'I saw the shark come out of the water and it was one of the biggest I've ever seen. I was pretty scared.'

Mr Verco, 24, was training for the Paddleboard World Championship next month and was about 80m from the incident when he immediately paddled towards the woman.

'I had to go, paddle up to her, and grab her arm and drag her in, paddling with one arm to the beach,' he said.

Before taking her to the beach he managed to raise his arms to lifeguards and form the 'X' code to sound the shark alarm and send out a craft.

He said it was one of the 'scariest things', paddling the woman to shore not knowing if the shark was coming back to attack again.

The woman remains in a critical condition in hospital but Nine News reported that she was conscious and was able to speak to paramedics as she was taken to hospital.

'I hope that she pulls through and I hope that she's able to make a full recovery and get to enjoy the ocean again,' Mr Verco said.

Off-duty lifesaver Ben Heenan was swimming near the shark attack and heard the woman's screams.

The president of the Coogee Surf Lifesaving club said he soon saw a huge pool of blood in the water and also went to help.

'As soon as I saw that I sped up to the lifeguards to make sure they were aware. They started to get some gear together and I ran down and grabbed one of their boards and started to paddle out,' he told the Sunday Telegraph.

'She was breathing … she wasn't talking but she wasn't unconscious. We started applying appropriate first aid, tourniquets, and the like.'

Emergency physician Dr Ian Ferguson was also enjoying a day off, walking along the promenade at Coogee, when he heard the screams.

'It was very close to the shore. It would have been the depth that kids would have been swimming in,' he told the Sunday Telegraph.

Dr Ferguson said the woman had substantial tissue loss from a '30cm bite' to her thigh.

Shark expert Dr Daryl McPhee, an associate professor in environmental science at Bond University, said it wasn't surprising that it was a great white.

'As the water cools around the Sydney region, you expect to see less bull sharks and more great white sharks,' he told Daily Mail.

'There's one thing that's out of character, which was that it occurred between the flags.

'That's an area where there's normally a lot more people, there's a lot more eyes on the water, there's surf lifesavers.'

Shark nets, about 150 metres long and set six metres deep, were removed from beaches in the electorate on April 30. They will be reinstalled by the council on September 1.

Dr McPhee said one shark attack does not directly correlate to moving the nets.