I am an F-1 student applying for 2010 H1B visa (waiting for decision)
I want to marry a green card holder through political ASYLUM.
I heard that it takes about 6months to get green card once applied because she got her green card after being an asylee. Is that true?

I believe you may be confusing USCIS case processing time with the total time for LPR approval.

Yes, it is taking approximately 6 months processing time to get permanent residence based after the case is file, but before you can file, there must be immigrant visa numbers available for that preference category, FB-2A, spouse of an LPR.

As of the most recent DOS visa bulletin, for most countries, they are working on cases with a priority date of January 15, 2005. So you can expect approximately 4.5 years before being eligible to file for PR.

During this time, the USCIS does not grant employment authorization nor travel authorization based on the I-130 or marital status. You will need to maintain your NIV status if you want to remain in the US lawfully during this time.

Consult with any immigration attorney, they can explain in more detail as to the specifics of your case. I trust this is responsive to your inquiry. Congratulations and good luck.