The company said it expects to raise as much as $250 million by selling an unspecified number of shares, and would use the money to help reduce its $3.1 billion debt.
It didn't say when it plans to go public, how many shares will be offered or the price it expects to get.
Norwegian is owned by three private-equity firms: Apollo Funds, TPG Capital and Genting HK.
Norwegian says they will continue to own a majority of the shares after the company goes public and will continue to control the board of directors.
Norwegian's main offices are in Miami but it is incorporated in Bermuda.
The company plans to trade on the Nasdaq under the ticker NCLH.
