The degenerative nerve condition is known to affect 125 people in the city and around 1000 across the country.
But despite this, sufferers have been wrongly accused of being drunk and thrown out of concerts and refused taxis because of a lack of understanding surrounding the symptoms.
At a full council meeting in Glasgow today, members will be asked to support a motion calling for a city action plan to raise awareness of Huntington's.
It calls on the local authority to work with health staff to educate people about the condition.
Huntington's Disease (HD) is a hereditary disorder of the central nervous system which can affect brain function and movement.
A child born to a parent with HD has a 50/50 chance of developing the condition. There is no cure.
Campaigner Annie McKenzie, who runs the Live for Live Foundation, has been working to raise awareness of the disease.
Annie, 45, from Bargeddie in North Lanarkshire, lost her father to HD, and one of her sisters is currently battling the condition.
Annie has been offered a test to see if she will develop HD but admits she is too scared to find out.
She will speak at the City Chambers today in support of the motion.
Annie said: "Many people with Huntington's are still afraid to admit that they have the condition.
"My sister was ejected from a concert in Glasgow because stewards thought she was drunk.
"She tried to explain that she had HD but became stressed which made her even more unsteady."
Sadie Clarke's husband James was diagnosed with HD in 1994 - he is now 60.
The mum-of-five from Sandyhills in the East End said not much has changed in terms of awareness in 20 years.
Sadie, 60, added: "People with Huntington's are unsteady on their feet and they can slur their speech - they can appear drunk.
"We need to change people's attitudes and educate them so that the next generation don't need to go through this."
Greater Pollok Councillor David McDonald, who has drafted the motion, said: "I hope it is the first step in improve the services and lives for those with HD.
"While there is no cure, there is a lot that can be done to improve and manage symptoms and I believe the council and our partners have a key role in ensuring that families living with the illness get the support they need and enable them to enjoy a high quality of life."