An Anglican priest who was caught having online chats about raping boys as young as two, and who once said he wanted to watch a man sexually abuse his own son while in a "pedo mood", has avoided jail.

Melbourne priest Philip Murphy, 54, pleaded guilty to using a carriage service to transmit child pornography over a series of explicit discussions he engaged in over Skype between December 2016 and February 2017.

Murphy, who worked in Sunshine in Melbourne's west, told police he used his position as a priest to gain the trust of the men he was chatting to online, sending them photos of his clerical collar.

Under the name 'pervert', he used the gay dating app Grindr to find other men who wanted to chat about sexually abusing children.

During one of the chats, a man discussed wanting to sexually abuse his own one-year-old nephew:

bi_1077: sis has a new baby boy should try and sit lol [sends picture file] Murphy: F*** mate. Sit the boy. You could visit me then if it was mid week and we could play How old is he bi_1077: 1 Murphy: Perfect…

In another of the online discussions, another man boasts about sexually abusing his sons.

Murphy responded: "id love to have slept with them when they were v yng".

He once told one man he was in a "very pedo mood", and told another he couldn't play "host" as he lived in a "church house", but that he could rent a motel room.

Murphy was arrested at Melbourne Airport on his return from a trip to Hong Kong in February 2017.

In sentencing, Judge Phillip Coish described the discussions as "grossly offensive and deeply disturbing" but said they related to sexual fantasies and not actual events.

"I accept there was no actual sexual activity with children, nor were any photos or videos of children involved," he said.

Judge Coish rated Murphy's prospects of rehabilitation as good and accepted he was genuinely remorseful.

Prosecutors had asked for an immediate term of imprisonment.

Instead, Murphy was convicted and sentenced to 12 months' jail wholly suspended, on the condition he is of good behaviour, is supervised by sex offender management for 12 months, and completes a sex offender program.

In a statement, the Anglican Archbishop of Melbourne, Philip Freier, said Murphy had been suspended from all church duties until the matter was dealt with by the church's professional standards board.

"I am profoundly saddened to hear of the Rev'd Philip Murphy's conviction for child pornography offences," Dr Freier said.

"By his actions, Mr Murphy has betrayed children and the trust invested in him to work as a priest of the church."