The number of people pledging their support has almost doubled since a petition was delivered to the health board last month.
Almost 8600 people have now backed the campaign, which is calling on NHS Greater Glasgow and Clyde (NHSGGC) to give a guarantee it will continue to fund the hospital.
Now known as Glasgow's Centre for Integrated Care, it is one of the few homeopathic hospitals in Europe with overnight beds.
NHS Lanarkshire is carrying out a review into funding for homeopathy at the hospital, at the Gartnavel site in the West End.
It follows a decision by NHS Highland two years ago to withdraw funding for referrals.
NHSGGC boss Robert Calderwood has previously warned that if other boards follow NHS Highland, he will have to look at how much the hospital costs the board.
Meanwhile, another petition has been launched, by a group called the Glasgow Skeptics, which is calling on the health board to withdraw all funding for the hospital.
Around 203 people have signed the petition.
The BMA's director of science and ethics, Dr Vivienne Nathanson, has previously said that "the funding of the homeopathic hospital should stop".
The hospital is one of four in the UK funded by the NHS and treats seriously ill patients using a combination of conventional medicine with alternative therapies, such as acupuncture.