ONLY CITIZENS can petition for their parents, so need to naturalize first. Green card holders are very limited in who they can petition, typically only a spouse or their own children,
QUOTE
Immediate Relatives of U.S. Citizens (IR): The spouse, widow(er) and unmarried children under 21 of a U.S. citizen, and the parent of a U.S. citizen who is 21 or older.
http://travel.state.gov/visa/immigrants/ty...types_1306.htmlQUOTE(fwaguy @ Sep 28 2007, 02:03 PM)

Yes you can, but as an LPR you will be subject to visa quotas and it could take years for your number to come up. USC's are not subject to these quotas so you may wish to look at getting your citizenship
LPR's can only petition for a spouse or their children.
QUOTE
Family Second Preference (F2): Spouses, minor children, and unmarried sons and daughters (over age 20) of lawful permanent residents. (114,200) At least seventy-seven percent of all visas available for this category will go to the spouses and children; the remainder will be allocated to unmarried sons and daughters.
http://travel.state.gov/visa/immigrants/ty...types_1306.html