Keith Pollock pounced on the 16-year-old stranger as she made her way home in the early hours of January 26 this year.
He battered the teenager before trying to force her into a darkened park in Milton of Campsie, East Dunbartonshire.
But Pollock, 50, fled when a delivery driver heard the girl's screams.
Pollock, who was jailed for rape in Australia in 1991, is now behind bars after admitting at the High Court in Glasgow to assaulting the teenager with intent to rape.
Lord Burns deferred sentencing for reports.