I just got my green card based on Asylum after waiting for about 6 years. My question is from now on can I travel out side of the USA using a passport from my country or I should still use Travel document until I become a citizen ?
Of course I am not planning to travel to my native country for is is not safe for me to go there.

Thanks for your advise on this matter.

This is just a test

If you have a green card, you dont need a travel document. You can travel freely.

When you *enter* a different country- you will usually need to use your own country's passport, although some countries specifically waive visas for people that have US green cards. To return you need only your green card. You would only need a travel document if you expect to be away from the country for a long time (typically more than 6 months). If that is the case I recommend getting advance parole to avoid losing residency.

A valid passport is always need to travel IN or OUT of the U.S. Depending on your status, you need some sort of "travel document" to get you back into the U.S. If you have a green card that is your travel document. Some people have valid visas. Some people do not have green card or a visa (like those whose AOS application is pending) they get an advance parole. But these travel documents do not excuse the requirement of a valid passport.