Any person crossing any international border is required to carry all the necessary travel documents with them in person. As a permanent resident of the United States, you must be responsible to carry valid travel documents that will not only take you out of the country, but will also bring you back into the U.S when you return from your overseas trip.
Departure Document Requirements
Passport issued by your home country - Even though you are a resident of the United States, your Green card is not enough to gain entry to other countries. You must carry a valid passport with you to enter other countries.
Your valid Green card.
If you have not yet received your Green card: You can still travel outside the country without any hassles. All you have to do is get your passport stamped with I-551 from the USCIS before you leave the country.
If you are in the process of application for Green card: You must file an Advance Parole document (Form I-131), if you have applied for adjustment of status or asylum in order to ensure that your application for Green card with the USCIS is not cancelled. The exception in this case would be if you possess a valid H-1, H-4, L-1, L-2, K-3, K-4, V-2 or a V-3 valid visa.
Re-entry permit - If your trip overseas will take a year or longer, you must apply for a re-entry permit (Form I-131) with the USCIS and obtain the document before you leave. The re-entry permit is valid for 2 years from the date of issue and you must return to the U.S while it is still valid. If you are a conditional permanent resident and your residency expires before the two years time period, you will be given a re-entry permit valid only upto the validity of your conditional residency.
Documents required to re-enter the U.S
You must carry your passport when you travel as it is a mandatory travel document. As a Lawful Permanent Resident returning back to the U.S, you must have one of the following valid documents in order to enter the country.
A valid Permanent Resident card or the Green card (I-551).
An I-551 stamp on your passport or on Form I-94.
A valid refugee travel document
A valid re-entry permit
Unexpired Immigrant visa.
If you lose your Green card while you are travelling outside the U.S
In the unfortunate event of losing your Green card, even stolen at times, you must inform the local police and obtain a report of your Green card stolen complaint, which will act as a document proof when you re-apply for your Green card replacement. In order to travel back to the U.S, you need to obtain a travel document called the Transportation Letter, issued by the U.S Government from the nearest U.S Embassy or Consulate.
This transportation letter enables you to travel to the United States, however, you need to complete an Application to replace your Green card, Form I-90, at the port of entry, (airport/border) and also pay the appropriate fee for processing the application.