Mr Muslim said the plan had been rejected by the Conservatives when they were in control of Bolton Council between 2019 and 2023.
“We didn’t think it was fair or reasonable for council taxpayers to pay any more for having a basic service,” he said.
“For residents in social housing, who often have gardens provided, they will also pay the new tax too.
“It’s another tax on the poor and vulnerable.”
Councillor David Grant, leader of Horwich & Blackrod First Independents said residents were “already struggling to pay the high council tax”.
He said the charge would lead to “an increase in fly-tipping” or people burning waste.
More than two-thirds of councils in England have already started charging for the garden bin service, including in Liverpool.
Mr Silvester, said the proposal had been put together with “extremely careful consideration” and would mean those using the service would contribute to the cost of providing it.
“Currently, over 80,000 households have free collections of garden waste and anyone who pays council tax helps to fund these collections, regardless of whether they have a garden or not,” he added.
A consultation on the scheme is available on the Bolton Council website until 4 November.