Stephen Jamieson, 28, is reported to have attached a pillow round his waist to avoid being injured by razor wire.
He was serving a 12-year sentence for armed robbery.
He is reported to have escaped after cutting through a gate at the back of a small secure exercise yard attached to his cell.
"He was able to get out of that exercise yard and then he had a range of bed sheets that he tied together and was able to swing them over the wall to then effect his escape by scaling that wall," New South Wales Corrective Services Commissioner Peter Severin told ABC News.
"It appears that he also had a pillow [that was] put around his waist and enabled him to make good his escape over the razor wire."
Commissioner Severin said Jamieson had a history of trying to escape and was put into solitary confinement after a man-made hole was discovered inside a workshop at the prison.
"He was clearly somebody that was in maximum security for all the right reasons and furthermore he was actually segregated in the maximum security section," he said.
The commissioner said that the escape was "a very serious matter" and would be the subject of an intensive security review because there was "absolutely no excuse for anybody being able to escape from maximum security".
A huge manhunt for Jamieson is now under way.
A maximum security prisoner has staged an audacious escape in the Australian state of New South Wales by tying bed sheets together to climb over a wall.