The Revd Peter Low, 65, downloaded a collection of images, some of which depicted the most serious category of abuse, Chelmsford Crown Court heard.
He pleaded guilty to three counts of possessing indecent images of children and one count of possessing prohibited images of children.
The Diocese of Chelmsford said it was "appalled" and online abuse of children "is not tolerated by the church".
Low, of Crescent Road, Heybridge, admitted possessing 55 indecent images, nine of which were said to be at the most serious level, and 124 prohibited ones.
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The clergyman, of the United Benefice of Heybridge with Langford in Essex, will be sentenced on 2 May.
As part of his bail conditions he must not have unsupervised contact with under-18s.
A spokesman for the Diocese of Chelmsford said Low remained suspended from all his duties as a vicar.
He would face a church investigation after sentencing, he said.
The spokesman added: "The diocese is appalled that a clergyman has fallen so far short of the standards expected by the church.
"The diocese strives to uphold the highest standards in safeguarding policy, training, practice and disciplinary action.
"The online abuse of children destroys childhoods and devastates society.
"It is not tolerated by the church."

Don and Maxine Simpson from Bakersfield, California, died four hours apart on adjoining beds, holding hands during some of their final hours.
Melissa Sloan said her grandmother died first and when her body was removed from the room, her husband followed.
"All Don wanted was to be with his beautiful wife. He adored my grandmother, loved her to the end of the earth," she told KERO-TV.
He was 90 and she was 87, and they met at a bowling alley in Bakersfield in 1952, getting married in the same year.
When civil engineer Don worked for the US Army, the couple spent some time in Germany, where they adopted twin 18-month-old boys from an orphanage.
They returned to Bakersfield, where she worked as a nurse and he owned his own engineering firm.
They are survived by one son and five grandchildren.

Bryony Nierop-Reading's home fell into the sea in Happisburgh, Norfolk, during the 2013 tidal surge.
She spent years battling with North Norfolk District Council which said she did not have planning permission to live in a caravan on a nearby field.
The 71-year-old has a home further inland but it is occupied by her daughter and son-in-law.
Bryony Nierop-Reading moved into her 1930s bungalow on Beach Road in 2008.
As the cliff-face eroded, virtually all of her neighbours moved out in 2010 after accepting compensation from the local authority.
But Ms Nierop-Reading refused and by 2013 her bungalow was left teetering on the cliff edge.
After losing her case with the district council, Ms Nierop-Reading's caravan was flattened.
She spent the weekend moving her belongings into a nearby container provided by the council.
"There's a lot of mess. I've already filled one six cubic metre container yesterday and I'm waiting for another to be delivered today. I'm in total shock", she added.
Ms Nierop-Reading said will be living in a motor home on a field she owns for the next week or so while she continues to clear everything up.
The council has been approached for comment.
A vicar has admitted possessing dozens of indecent images of children.
[NEXT_CONCEPT]
Even in death, a couple married for nearly 62 years were inseparable.
[NEXT_CONCEPT]
A woman whose bungalow was destroyed by the sea has moved out of her temporary home after losing a planning row.