If your green card has been lost, stolen or destroyed, you will need to file Form I-90, Application to Replace Permanent Resident Card.
For more information, read My Green Card Was Lost or Stolen.
If your green card has been lost, stolen or destroyed while traveling outside the United States, you will need to obtain a transportation letter or boarding foil to return to the U.S. on a transportation carrier. U.S. law requires transportation carriers like airlines to make sure all passengers traveling to the United States be in possession of a valid passport and any required visa. You can obtain this essential travel documentation by filing Form I-131A, Application for Travel Document (Carrier Documentation), at the nearest U.S. Embassy or U.S. Consulate.