Families who visit the site at St John's Church in Heath Hayes complained to the council.
Bosses at Cannock Chase Council are set to agree at a meeting this week to formally adopt the graveyard from the Parochial Church Council.
They are proposing to fast-track the transfer of the graveyard so the clean-up can begin, which will cost £10,000.
Efforts had been made to transfer the graveyard from the church to the council several years ago but the process has held-up due to the procedures that need to be followed in such cases and it has resulted in the site becoming overgrown.
In a report to cabinet, which meets on Thursday, head of commissioning Mike Edmonds, says: "The council's involvement in the maintenance of closed churchyards is a statutory requirement.
"Making places more pleasant and attractive will benefit the whole of community.
"A rough estimate of the cost of works required to bring the churchyard up to an acceptable standard is £10,000.
"An ongoing budget of £3,500 will also be required to undertake an annual maintenance regime of the churchyard."
The report adds that Heath Hayes and Wimblebury Parish Council is hoping to take on responsibility for the maintenance of the churchyard, which closed to new burials a number of years ago.
Cannock Chase Council spokesman Jamie Summerfield said the transfer of the graveyard was a 'complicated procedure'.
He said: "St John's Church acted properly in passing on responsibility for maintenance of the graveyard in 2011/12 but the transfer process has taken longer than usual and maintenance of the graveyard has fallen through the cracks.
"Cannock Chase Council is now working urgently to complete the process of adopting the graveyard so that grounds maintenance work can be carried out and the graveyard brought back into an acceptable state.
"A report will be going to the council's cabinet on Thursday to seek formal adoption of the graveyard.
"If approved, the council will then start to maintain the graveyard."
Relatives visiting graves at St John's Church previously complained that the grass had not been cut for months.
Rosemary Whitehouse, aged 56, of Boston Close, Heath Hayes, visits the graves of various members of her family. She said it broke her heart seeing the place in 'such a state' and she was forced to use a pair of shears to trim the grass around the headstones.