Queen's Cross Hous-ing Association is to increase rents by 4.6% in April – following a 4.5% rise last year.
Residents say the increases, totalling more than 9% over two years, are unfairly high at a time when wages are frozen and benefits are being cut.
And they claim the housing association has not carried out improve-ments to the flats to justify the hike.
A Facebook page has been set up and the campaign group has been distributing leaflets to residents to gather support for a petition.
Queen's Cross says the increase is needed to meet the increasing cost of contractors and materials and to continue to provide an "effective" service for tenants.
Residents held a meeting last week to confront housing association managers about the rise.
Alice Coy, 37, a bank nurse, who has lived at the Cedar Street high flats for nine years, said the rises will increase her monthly rent by £30.
She said: "We under-stand that rents have to rise but this is unaccept-able when you consider most people are going through a pay freeze.
"When Queen's Cross took over they were full of promises. But nothing has come through. A lot of the flats in my block are damp and the lifts are constantly breaking. Most people have been stuck in the lift.
"We were promised re-cladding but that hasn't happened.We have storage heaters which are expensive and I can't afford to run them in the evenings. I can't work more hours."
Queen's Cross director of housing and customer services Fin McElhinney said the association was consulting with tenants on this year's rise.
She said: "Like all social housing providers our challenge is to maintain and improve tenants' homes and deliver services while managing the significant impact of both public spending cuts and welfare reform.
"We are looking carefully at the effect that different levels of rent would have on the services we could provide to tenants.
"We're listening to what our tenants are saying to us during this consultation period and will take everyone's views into account as part of the rent setting process."
Queen's Cross is responsible for almost 4500 homes in Woodside, Hamiltonhill/Wester-common, Queens Cross and Dundasvale.