Coun James Gibson, who represents Weetwood, has launched a petition calling for the site to be made secure, claiming parts yet to be developed are “incredibly dangerous”.
The petition, which claims that the site has become a hotspot for anti-social behaviour including fly-tipping, starting fires and underage drinking, has been signed by nearly 200 people since its launch last Friday.
Coun Gibson said: “Children and young people from all over the area have been trespassing on this very dangerous site. It’s only a matter of time before a tragic accident occurs.”
Just last week, firefighters were called to tackle a blaze at the hospital building, which closed in 2007.
Coun Gibson said: “The community is very worried that young people are accessing the site and are in real danger. Of course, the people that live around the area are also suffering from anti-social behaviour and worried about fires potentially spreading and noise nuisance.”
Leeds-based Chartford Arthington is in the process of regenerating the hospital site and company director Matthew Fuller told the YEP in March that the firm bought it in 2011 after the NHS put it on the market amid the move to a new oncology unit at St James’s Hospital.
A planning application to Leeds City Council to convert the former hospital building into 21 houses and nine apartments, has yet to be decided.
The YEP has made attempts to contact Chartford for comment.
North West Leeds Neighbourhood Policing Team Inspector Andy Loftus said the police were aware of security and anti-social behaviour issues at the hospital site and had been working with all parties to try and improve security there.
He said the developers had already put some security measures in place at the “large and vulnerable site”.
He added: “Officers are also carrying out joint work with firefighters and local schools to educate children on the dangers of playing in disused buildings and will be carrying out a joint schools talk next week.
“The Leeds North West NPT fully appreciate residents’ concerns about security at the site and we will do all we can to try and resolve this issue.”
A Leeds City Council spokesperson said representatives of the authority had met with the site developers and discussed measures that could be taken to reduce anti-social behaviour.
In a statement, the council said: "Following a constructive meeting, the developer agreed to improve security at the site by increasing security personnel present and boarding up the hospital building.
“We will continue to monitor the situation and work with the developer around this particular issue."