Can a green card holder apply for a fiance visa?

Fiance visas are only for fiances of U.S. citizens, not green card holders. In order to bring your fiance here, you will have to get married first. You will then have to file an immigrant visa petition for your spouse, known as Form I-130, and wait for it to be approved and for a visa to become available. The best alternative would be to naturalize and become a U.S. Citizen, so that you have the K1 Fiancee visa benefits.