The man, who is in his 70s and was identified only by his initials A.F., can be heard in the video recorded with a hidden camera apologising to one of the victims he abused in the 1980s.
"I don't know why I did it...it was like a child's game," he says in the video posted on the website of Barcelona-based daily newspaper El Periodico de Catalunya which masked his face.
The victim said he was sexually abused by the former teacher dozens of times when he was 8-14 years old. His allegations were not refuted by the former teacher.
The abuse took place at a Marist school in Les Corts, a Barcelona neighbourhood, at the centre of a paedophile scandal which erupted in February after the paper published the confession of a former gym teacher who said he had sexually abused his students.
The teacher spoke to the newspaper before being questioned by a judge who is investigating complaints of sexual abuse filed by five families against him.
The newspaper article triggered a wave of fresh complaints. There are now a total of 29 complaints against six former teachers from three Marist schools in Barcelona.
Three of the former teachers, including the man featured in the video released on Monday, have confessed.
The Archbishop of Barcelona, Juan Jose Omella, apologised to the victims, in an interview published on Sunday in El Periodico de Catalunya.
The Marist community - a Roman Catholic teaching order - did not know of the abuse until now and followed the protocols in place as to how to deal with such cases, he added.
The scandal has caused outrage in Spain, where there have been few sexual abuse scandals involving the Church.
The biggest case to date erupted at the end of 2014 when a former altar boy complained of having been molested as a child by priests in the southern city of Cordoba, in a case which drew the attention of Pope Francis who was vowed "zero" tolerance for paedophilia.
Ten Catholic priests and two laymen were initially charged over the case, although eventually charges were dropped against all but one of them, on the grounds that too much time had passed since the alleged crimes took place.