An extra £19.25m has been set aside for the cost of the over budget Norwich Northern Distributor Road - but council bosses have said they cannot guarantee the final bill will not exceed £205m.
And if the council were to borrow £12m to cover part of the bill it would cost £425,000 a year for the next 40 years.
Norfolk County Council officers had sought the extra money for the road's budget on top of the £185.7m already budgeted.
Officers said the extra money was needed after contractor Balfour Beatty claimed for extra costs accrued in building the 12.5 mile road, which will stretch from the A47 at Postwick to the A1067 Fakenham Road.
The council spent months locked in talks with the contractor over the price hike, with issues such as delays in getting the go-ahead to take the road over the railway line at Rackheath and the cost to divert utilities, such as gas pipes, pushing up the cost.
At today's meeting of the council's policy and resources committee agreed to add an extra £19.3m to the NDR budget.
They will re-allocate £7.3m from the budget for capital projects and £12m from cash balances.
A long-term capital funding arrangement to replace that £12m will be submitted to the policy and resources committee in January.
Officers said, if the council were to borrow that cash, based on current rates that would cost about £425,000 a year for the next 40 years.
Steve Morphew, leader of the Labour opposition questioned how the soaring costs of the road had been monitored and why councillors had not been informed more regularly of the increases.
Officers said the right processes had been adhered to.
With questions over why the council had not agreed a fixed price contract at the start, officers said that would have seen the council pay a premium of some 30pc, while the target based contract which was agreed was about 14pc over budget.
And Conservative councillor Rhodri Oliver said that had effectively saved the council millions of pounds.
But Mr Morphew said: 'My anxiety remains about how we got here. What I have heard is that it was inevitable, but £25m is a hell of a lot of money and I'm not prepared to accept that was inevitable.'
And when asked if the £205m figure would be the final bill, Tom McCabe, executive director of community and environmental services, said he could not give that assurance.
He said: 'I have been very careful to say the contract remains live.
'There could be gains and there could be losses.
'We would hope that the winter is kind to us, but until we get to end we cannot he sure and it would be foolish for me to give that assurance.'
The section of the NDR from the A1067 to the A140 Cromer Road has opened and council bosses still hope the section from the A140 to Wroxham Road could open before the end of the year, with the remaining part open in March next year.
The council already made the western link - which would connect the NDR to the A47 to the west of Norwich - a priority.
But Green Party councillors in Norwich have put forward a motion, to be debated at Norwich City Council tomorrow for City Hall to oppose the western link and to get a commitment for bus rapid transit (BRT) corridors to be delivered.
Green councillor Denise Carlo said: 'When the NDR was approved, we were also promised a modern bus system. There is little sign of progress on BRT, apart from the first phase along Dereham Road.
'It is simply scandalous that new road schemes are being prioritised ahead of efficient bus services.'
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