The report - based on an interview with the church's top exorcist, the Rev. Gabriele Amorth - came a day after the pontiff warned Roman Catholics to beware of the daily temptations of the devil.
John Paul's most recent exorcism took place in September, when he tackled the demons possessing a 20-year-old woman, Amorth said.
"This girl was rolling around on the ground," he said, describing her condition as "very serious - a series of curses."
"People in the Vatican had never seen anything like it," he said, but added, "For us exorcists, it is run of the mill."
A year earlier, in September 2000, the pope performed an exorcism on a 19-year-old woman who flew into a rage during a general audience in St. Peter's Square.
Press accounts at the time described how the teen screamed incomprehensibly in a deep voice and fought with super-human strength when Vatican guards tried to subdue her.
In the first exorcism performed by John Paul, in 1982, he drove the devil from a woman who was brought to him writhing on the ground, according to a published report.
In last Sunday's address, the pope urged his followers to beware Satan's "insidious actions."
"Each and every man . . . is tempted by the devil when he least expects it," he warned.
The Vatican, blaming Satan for many of the modern world's ills, updated its exorcism rules three years ago, for the first time since 1614.
In an 84-page manual, it outlined the symptoms of diabolic possession - including speaking unknown languages and having superhuman strength - and said not to confuse them with psychiatric problems.
