Bristol City Council's cabinet has backed plans for a council tax rise of almost 6%.
The cabinet has agreed to limit the rise for a band D property to 5.9% compared with a 7.2% rise in 2003.
In a statement, the council said it had taken £1.18m from its coffers to help reduce the increase.
Councillors met on Friday evening to set the figures, which will be discussed and voted on at a full council meeting on 2 March.
The proposed budget would mean people living in a band D property would be charged £1,084.46 for council services, an increase of £60 on last year.
On top of that, householders in Bristol will also face a levy from the police and fire services.
Councillor Barbara Janke said: "We have fully passported all additional funding on education.
"However, additional costs for social services for vulnerable people were not funded by central government and these extra costs would have to be passed on to the taxpayer."