Does a Green Card holder living abroad need to pay taxes?

As a permanent resident (greencard holder) you are required to file a tax return whether you are living in the US or not. You must report your worldwide income and, if necessary, pay any taxed. However, you may be entitled to the foreign earned income exclusion which could eliminate any income tax.

Lanny K. Williams, CPA Nawarat, Williams & Co., Ltd. Income Tax Services for Expatriate Americans

There may also be a Foreign Tax Credit. Between the two, there's a good chance you owe nothing - but you must file. Trust me, you'll be glad you did file when Immigration tries to lift your Green Card some day on the basis that you've abandoned your US residence by living and working overseas....

Doug

A correct statement would be that greencard holders are required to file under the same conditions as US citizens, that is, if their total income exceeds a certain amount or their income from self-employment exceeds a certain amount, etc.