Vancouver's Park Board wants to dismantle the camp of about 250 people, alleging it is out of control as a result of drug use, violence and a lack of leadership,
The city says it has offered all of the residents spaces in homeless shelters.
The injunction has been opposed by the Pivot Legal Society, which is representing the camp residents.
Pivot argued in court earlier this week the campers have a Constitutional right to remain in the camp because it is safer than living on the streets or in homeless shelters.
The homeless campers began living in Oppenheimer Park in the summer to highlight a lack of affordable housing.
In late September the city asked the court for a legal injunction to allow it to move in and dismantle the camp because of health and safety reasons.
Justice Jennifer Duncan is expected to issue a ruling at 1 p.m. PT.