The woman claims to have met the BBC DJ at a Manchester disco in 1966 when she was just 15 and he invited her to his flat in Salford, where they regularly met and had sex.
The victim, now 62 and from Manchester, said on one occasion she recalls Savile was dis-appointed she had changed out of her school uniform.
The mother of two wants Savile, who died last year aged 84, to be stripped of his knighthood.
She said: "To hear him still described as Sir Jimmy Savile and still celebrated for his charity work is a slap in the face to those of us he used. I was 15 when we started, but 15 in 1966 was probably like nine today.By the time I turned 18 and was more like a women, he lost interest and denied even knowing me."
She is one of 60 victims to have come forward whose cases are being looked at by police.
Officers think the DJ and television presenter may have abused victims for decades.
The BBC and other bodies could be sued by victims if it can be shown they were negligent in allowing Savile to prey on young victims.
Former High Court judge Dame Janet Smith will lead the BBC's internal inquiry into the sex abuse claims. There is also a Department of Health investigation into Savile's conduct during his charity work at three hospitals – Stoke Mandeville, Broadmoor in Berkshire, and Leeds General Infirmary.