Ivor Gifford from Abertillery sent explicit messages to fake profiles set up by a group called The Hunted One, which claims to "hunt sexual predators".
He claimed he believed everyone on the site was over 18, but a jury at Newport Crown Court found him guilty.
Sentencing will take place on 2 June.
The court heard two profiles 'Jessie' and 'Jodie' were contacted by Gifford.
He repeatedly sent messages and made comments which were of a sexual nature despite being told several times by those behind the profiles they were 11 and 12.
Owen Williams, prosecuting, said: "He was persistent in his attempts. In over 100 pages of messages, you will see that the vast majority refer to a sexual act.
"Mr Gifford graphically describes sexual acts. He sent images of himself naked."
The court heard the chat logs described Mr Gifford asking if the person he was speaking to had reached puberty yet, and if she would "dress sexy" if they met.
Mr Williams continued: "He then went a stage further, having groomed online he made arrangements to meet her.
"Directing a child, who doesn't know how to get from Cardiff to Abertillery, how to get a bus then a train."
Two members of The Hunted One confronted Gifford at Llanhilleth train station, where he had arranged to meet his online contact.
The police were then called and Gifford was arrested.
He had denied inciting a child under 13 to engage in sexual activity and a charge of online grooming but a jury deliberated for around an hour before finding him guilty.
Det Supt Leanne Brustad, head of public protection for Gwent Police, said while officers relied on members of the public to detect crime, it was important not to cross the line into vigilantism.
"Revealing the identity of suspected paedophiles gives the suspect the opportunity to destroy evidence before the police can investigate them," she said.
"It also leads to people who have been identified going missing or raising concerns for their safety.
"This can divert significant resources into protecting suspects, which would be better invested in investigating and, where there is evidence, prosecuting them."

The 25-year-old former Celebrity Big Brother winner and Geordie Shore cast member was stopped for driving erratically in Newcastle in January.
The city's magistrates heard she had earlier been drinking on a train home from London to Tyneside.
The court heard the conviction would scupper plans for a career in the US.
Crosby, who admitted the charge, was also ordered to pay Â£1,185.
Magistrates were told Crosby's Range Rover was seen weaving down the road by two police officers in the early hours of 28 January.
When she was pulled over, a breath test showed she had 80 microgrammes of alcohol in 100 millilitres of breath, compared with the legal limit of 35.
The court heard because she also had been banned from driving for 18 months in 2012, she would not be able to get a visa to travel to the United States, where she had planned to work.
Nick Freeman, defending, said Crosby had decided to make the short journey from the railway station to her hotel despite having initially planned to get a taxi.
He said: "She accepts that she is the author of her misfortune and is bitterly ashamed, contrite and embarrassed."
He added his client had been close to landing a TV career in America but "that will not now happen as she will not get a visa".
Banning Crosby, chairman of the bench Keith McIntosh said it "beggared belief" that she had been caught for a second time.
"We take drink-driving offences very seriously in this court, even more so when it's not the first offence," he said.
Crosby, from Sunderland, won Celebrity Big Brother in 2013 and appeared in all 11 series of Geordie Shore.
A 92-year-old man has been found guilty of using a chatroom to incite what he believed were 11 and 12-year-old girls to engage in sexual activity.
[NEXT_CONCEPT]
Reality TV star Charlotte Crosby has been banned from driving for three years after being convicted of a second drink-driving offence.