Coun Peter Box confirmed the authority is likely to put a two per cent precept on council tax bills as it revealed it has to save £27 million in the coming year which could include 200 jobs cut.
The precept to help pay for elderly care costs is on top of a likely 1.99 per cent rise in the council tax.
However, while the precept - a new power given to councils by the government - will raise £2.1m it will still leave a £4.5 million gap in the social care budget as demand and costs rise.
A recent report showed Wakefield has one of the highest percentages of working age people close to retirement.
Coun Box said: “Everybody in central and local government knows of the increasing pressures in adult social care. We know that the over-85s are the biggest growing demographic and we know it is this group that most needs care.
“That’s an issue right across the country and in Wakefield that is exacerbated because we have an increasing ageing population so there are huge pressures on us.
“Whilst I am glad the Government have recognised the problem I am not sure they fully understand the cost and that what they have proposed won’t really address the problem.”
While the authority will make significant budget cuts this year it has also set out plans to invest £200 million in areas including roads, schools and leisure facilities.
Coun Box said: “I hope people will recognise we are being even more efficient, we are trying to deliver better services and doing things differently.
“We have got to be positive about what we are able to provide.”
The council’s cabinet will discuss the budget on February 16 before the full council meeting on March 2.