The 45-year-old Australian actor spoke while in Beijing to promote his latest movie, "X-Men: Days of Future Past."
Jackman, who plays Logan and Wolverine, wore a bandage on his nose after having a basal cell carcinoma removed last week. Basal cell carcinoma is a slow-growing form of skin cancer and Jackman was treated for the same disease last year.
He told The Associated Press: "I'm realistic about the future and it's more than likely that I'll have at least one more but probably many more, which is not uncommon for an Aussie particularly from English stock growing up in Australia where I don't remember ever being told to put sunscreen on."
He added: "But the beauty of this is it's all preventable, it's just about getting proper check-ups. I can be typical man, a little lazy, I couldn't be bothered and now I'm not lazy at all."
"X-Men: Days of Future Past" will be released in China and the United States on May 23. It has an all-star cast, including Jennifer Lawrence, Halle Berry and Patrick Stewart. It is the seventh film in the mutant superhero blockbuster franchise that has grossed $2.3 billion worldwide.
Jackman, who has appeared in every X-Men movie over 14 years, travels back to 1973 to change history and save humans and mutants from destruction.
While Jackman previously said that he was pretty sure he wouldn't act in any further X-Men movies after the next one, which is scheduled for release in 2017, he told the AP: "I think I might have overplayed my hand a little bit by saying I'm almost sure that the next one will be my last."