Taming the Tiger detailed how Mr Anthony was taken to China by his grandfather, a kung fu grand master, where he endured beatings during training to eventually become a three-time martial arts world champion. After moving to Cyprus he was hired by businessmen, gangsters and diplomats as a bodyguard.
After a conviction for theft, he found God while in prison in Nicosia.
The book was translated into 25 languages and more than 1.5 million copies were distributed worldwide.
But holes began appearing in the story after an internet campaign by a group of Christians who doubted its truth, including New Zealand evangelist Julian Batchelor.
NZ Christian Network's sister organisation, Evangelical Alliance UK, investigated and concluded that "large sections of the book Taming the Tiger, and associated materials, which claim to tell the true story of Tony Anthony's life, do not do so".
Mr Batchelor said he believed Mr Anthony would be in New Zealand - where his story and controversy were unknown - for about six weeks to try to rebuild his profile.
In July, Britain's Observer newspaper said Mr Anthony had claimed his kung fu world titles were in competitions so specialised as to be unknown by outsiders. But some material was copied from a martial arts website, and one passage was lifted from a book about Bruce Lee.
Auckland woman Lyn Rule is organising Mr Anthony's tour. She would not reveal his itinerary.
"He's just come over to do what he does, and that's to spread the gospel ...
"I know the whole story. When you get parts of it like what's happening, people jump to a lot of conclusions. I haven't jumped on that bandwagon."
Mrs Rule has co-ordinated events for Elim Christian Centre in Botany, but said she had brought Mr Anthony here in a personal capacity.
A spokesman for the Elim Church said it was not hosting any events involving Mr Anthony.
Mr Anthony could not be reached for comment. However, on his website, he said Taming the Tiger was not intended to be a "strict historical account of each and every event with supporting minutiae".
He said that since writing the book he had discovered more information about his family history.
"I now fully accept that there are a number of details that appear in the book which are no longer historically accurate."
British evangelist Tony Anthony:
• On moving to China aged 4, and being trained in kung-fu: "My grandfather used to raise me with the bamboo cane ... He'd rush into my bedroom in the early hours of the morning with a bucket of ice-cold water and throw it over me, and that was his way of waking me up to go into the courtyard and do training."
• On working as an elite bodyguard: "Instead of shooting people in the arm or the leg, I'd shoot them in the face."
• On life in prison: "They put me in a cell with seven bunk-beds, I was the fourteenth man. And everything that you can imagine that one man can do to another man was happening in that cell that day."
