No. Permanent residents cannot petition for parents; only US citizens can.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.
You will need to naturalize (become a United States Citizen, not just a Lawful Permanent Resident), and be over the age of 21 before you can petition for your parents.
Obtain a consultation from a local immigration attorney so they can ask the right questions in order to give you the most accurate answer. Immigration law is complicated and it is difficult to give definite answers via a public forum.
Thomas J. Baker
Law Office of Daniel M. Wigon
816 H Street Suite 108
Sacramento, CA 95814
820 Alhambra Ave
Martinez, CA 94553