Cornwall County Council has been told it is not making adequate improvements to the services it provides, the Audit Commission said.
It was one of only 4% of councils in England told it was not improving enough in key areas including its children's services.
The council has been awarded a high rating of three out of the maximum four stars by the commission.
A spokesman said changes had already been made.
The Audit Commission report stated: "The council is improving in some areas but many key services are not improving.
"Improvements in support for older people to live at home are inconsistent.
"Some aspects of children's services, including school placements, have not improved and the number of people killed or seriously injured on roads has increased.
"It is poor at setting its priorities... and performance management remains weak."
Council leader, David Whalley, said: ""We are pleased that Cornwall County Council is recognised as being good overall, but this is not good enough.
"We want to establish Cornwall as a high performing council which is providing high quality services to local people.
"We have already begun to tackle the issues identified in this report and I am confident that, with the support of local people, we will achieve our aim within the next four years".
Cornwall County Council will merge with the six district councils at the end of this month to form a new unitary authority, to be known as Cornwall Council.
Mr Whalley, 65, has confirmed he does not wish to be leader of the body, saying it is a job for a younger person.