Keith Collard, 24, from Enfield, north London, shook and almost fell backwards in the dock as the jury of seven men and five women convicted him of the murder of Katrina Monk.
He admitted manslaughter but denied the murder charge, claiming he had not intended to kill Katrina.
Collard ambushed Katrina with an imitation firearm as she took a short cut home from school down an alleyway by his back garden. Her body was found in nettles in the alley the next day, with a plastic bag taped over her head. Collard had suffocated her.
Collard claimed he had not intended to murder the schoolgirl after pouncing on her from behind and holding a replica Browning automatic pistol to her head.
He then dragged her, while she screamed and struggled, into his garden shed. He told the jury he wanted to satisfy his sexual urges and touch her body.
'I started to touch her on her thighs and her breasts. That is when she started to scream,' he said. He masturbated on her. Afterwards she made for the door still screaming and he put his arm around her neck to try to stop her screaming. But the jury decided he deliberately killed her to silence her.
Obsessed with sexual fantasies, computer games and soft porn, Collard would sit for hours in the solitary loneliness of his room.
When not playing with his computer games or reading 'girlie' magazines, he spied through his binoculars at schoolgirls as they took the short cut down the alley by his home in Bradley Road.
He had had sexual intercourse only once - with a casual pick-up while on holiday. His only long-term relationship with a girl ended two years before the murder and sex had never taken place, the court was told.
The Common Serjeant of London, Judge Neil Denison, told the jury during his summing-up: 'You may think a combination of sexual repression and a fascination for weapons is a potentially dangerous combination.'
Collard - who had never been in trouble with the police before - admitted after his arrest that he had a fetish for taking women's knickers from washing lines near his home.
Police found nearly 40 pairs in his bedroom at the house he shared with his mother, a solicitor's secretary, and his stepfather, a van driver. Collard said he had few friends and after cashing his Giro cheque at the Post Office spent all day alone in his room playing computer games.
When he went to repair his garden gate, he spotted another schoolgirl walking down the alley.
He had a sexual urge to touch her body, he said. After pacing the garden he returned to his room and collected the gun.
'I wanted to scare a girl with it - I wanted to touch woman's body. I was going to satisfy my sexual urge by touching a girl and masturbating,' he said.
Although Collard maintained he had not meant to kill Katrina, the Crown's pathologist said that the signs of asphyxia were compatible with compression on her face and neck.
Police found that under the bag her face was partly covered with a bandage and sticky tape mask.
Her skirt was up, her hands bound in front of her, her tights were down and her breasts and buttocks exposed. But there were no signs of sexual interference, although semen was found on her underclothes, the court heard.