If I am a green card holder my mother is in the US with B2 visa and I want her to stay, can I petition for her green card?

There is no visa category by which a Permanent Resident may sponsor a parent for adjustment of status, although there is for a U.S. citizen to sponsor a parent. Of course, many other details beyond the parent/child relationship determine eligibility. It would be wise for you and your mother to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.