Can I apply for green card if my wife is a permanent US resident? I have F1 visa. my wife will be a citizen by 2019.

No. She can petition for you but the priority would take about two years to become current. Only the will you be able to seek either an immigrant visa or adjustment of status as the situation could require.

She can sponsor you, but it will 18-24 months before you will be allowed to apply for a green card.
Please see https://www.avvo.com/legal-guides/ugc/green-cards-for-family-members

It depends on your priority date. When did your wife file the I-130?
Also, how and when did your wife get her green card? And when did you get married?

If you are currently in the United States and are one of the specified categories of relatives of a permanent resident, you may be able to apply for a permanent resident in two steps.
Step One – Your permanent resident relative must file Form I-130, Petition for Alien Relative, for you and it must be approved. You must wait for your priority date in your immigrant visa category to become current.
Step Two – Once the priority date in your visa category is current, you may file for adjustment of status with Form I-485, Application to Register Permanent Residence or Adjust Status