Does permanent resident need tourist visa to visit the Caribbian?

Whether or not you'll need a Visa depends on which country you're a citizen of and the countries in the Caribbean you plan to visit.

For example, if you're a UK citizen and have a UK passport, Visas are not required for entry to the Caribbean countries (I'm not sure about Cuba's requirements).

The best way to check is to do a search for Tourist Visa requirements for the country you plan to visit. Each country has a listing on its Embassy website with the requirements for citizens of every other country.

As a note, cruise ships do not issue Visas -- and if one is required, you will not be allowed to board the ship.