The actor's character in the film, Hannibal Smith, constantly smokes cigars. Neeson was given prop cigars to use at the beginning of filming, but he later switched to the real thing, reports The Sun.
"I stopped smoking 16 years ago so it was a real issue for this movie," he said.
"The prop guys got me these amazing fake Cuban cigars but then I was given real ones. I said, 'I can't do this, I'm an addict'. By day two of filming I had discovered cigars and I was in trouble."
The 58-year-old added that he would have to insist on using rubber cigars if he appears in a sequel.
The A-Team opens this Friday in US cinemas.