Peter Low, 65, pleaded guilty to three counts of possessing indecent images of children and one count of possessing prohibited images of children at Chelmsford Crown Court on Wednesday.
He has been suspended from all his duties as a vicar of the United Benefice of Heybridge with Langford in Essex.
Police had found Low, of Crescent Road, Heybridge, had nine images that were at the most serious level, category A, with 25 category B images, 21 category C images and 124 prohibited images of children.
All counts relate to July 27 last year.
Low, who has short grey hair and wore glasses, a dark blue suit, white shirt and red tie, was bailed to appear at Chelmsford Crown Court on May 2 for sentencing.
Judge Christopher Morgan said this was to allow for pre-sentence reports to be prepared.
One of Low's bail conditions is that he must not have unsupervised contact with under-18s.
A spokesman for the Diocese of Chelmsford said Low remained suspended and would face a church investigation under the clergy discipline measure after sentencing.
"The diocese is appalled that a clergyman has fallen so far short of the standards expected by the church," the spokesman said.
"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.
"We are offering pastoral support and are keeping all those affected by the situation in our prayers."