Merlin Entertainments, the UK company that owns Legoland, Madame Tussauds and Chessington World of Adventures, says it plans to issue shares to the public.
Merlin operates 99 attractions in 22 countries, and has 54 million visitors to its parks a year.
It says it is the second-largest company of its kind in the world after Walt Disney.
Its other well-known attractions include Alton Towers, Thorpe Park and Warwick Castle.
The business has a turnover of £1bn a year and is thought to be worth some £3bn.
The share offer, which will see 20% of the company pass to public investors, is accessible to smaller shareholders with a minimum investment stake of £1,000. Shareholders will also get a one-off 30% discount on certain entry passes for Merlin's theme parks.
The company, which was formed in 1999, says the number of visitors to its parks has grown by 11% a year since 2008.
The company's non-executive chairman, Sir John Sunderland, said: "I have been impressed by the significant growth that Merlin has delivered as a private company.
"But there is more to come and I believe Merlin has a very promising future as a publicly listed company."