Peter McGinnis, 48, met the teenager at the school he taught at and befriended the boy and his family.
He took them on trips in the school holidays and took the boy on overnight stays to a hotel and a log cabin.
McGinnis denied the allegation and claimed he was a "friend of the family".
After a trial at Glasgow Sheriff Court, McGinnis, from Glasgow, was found guilty of sexually grooming the boy between June 2009 and March 2010.
Sheriff John McCormick told McGinnis that because of the "insidious" nature of the charge and as he was a teacher who "inveigled" himself in to the family a custodial sentence was almost inevitable.
The court heard McGinnis first met the teenager when he taught him English.
Near the end of the school term in 2009, McGinnis offered to give the pupil extra help on work.
Soon he was helping the boy with school work, bringing the boy to his South Lanarkshire home where he spent time alone with him and was also getting close to his family.
The teenager claimed he would go to McGinnis' home where they would drink alcohol and he went away overnight with him on two occasions and that they shared a room.
McGinnis told the jury: "I was a friend of the family I wasn't there in the position as a teacher."
Procurator fiscal depute Cassie Scott asked: "Do you find it appropriate to take one of your pupils away for the night to a log cabin?"
He said: "In the circumstances at the time I found it appropriate."
The former teacher denied taking alcohol for the boy to drink during the overnight stay at the cabin, but the jury was shown a photograph of the teenager holding a bottle of beer.
He confirmed he also took the teenager to a hotel for the night and shared a room with him on that occasion.
The court heard that in March 2010 the boy told a family member what had been going on.
Sentence was deferred until next month and McGinnis was remanded in custody.
He was also placed on the Sex Offenders register.