How can I get a re-entry permit if I am a US immigrant but wants to go back to my country for a while?

As long as you have a valid passport and green card, you are permitted to travel aboard and return to the United States without any additional documents. To maintain your legal residency and eligibility for naturalization, you should return and reside in the US for 6 months each year.

You may apply for a re-entry permit on Form I-131. The processing time is about 3 months. You can have the reentry permit mailed to your home country if you need to leave before you can get it, but you have to make sure you do the biometrics first. You may still qualify for naturalization even if you are gone for more than a year, as long as you can meet the at least 50% physical presence requirement and you have no intention of abandoning your permanent residence in the US.