Wendy Knell, 25, was found dead in her bedsit in Guildford Road, Tunbridge Wells, on 23 June 1987.
Her father, 82-year-old Bill Knell, who has cancer, said: "I want to know, why did he have to kill her?
"They can't do any more for me and I would really like [her killer] caught before the end comes."
Pam Knell, Wendy's 80-year-old mother, said she still kisses a photograph of her daughter every time she leaves her home in Tonbridge.
Kent Police have a full DNA profile of Miss Knell's suspected killer but have never found a match.
A police spokesman said detectives had found there were no clear signs of a forced entry and no one else who lived at the bedsit had heard anything unusual.
Her keys and diary were missing and have never been found.
Miss Knell's murder is being linked to that of 20-year-old Caroline Pierce five months later on 24 November, 1987.
Ms Pierce, also from Tunbridge Wells, was found dead on Romney Marsh.
She had last been seen in Grosvenor and Hilbert Park. Her keys were also missing.
Both women had worked in Camden Road in Tunbridge Wells.
A Kent Police spokesman said both investigations remained live and detectives were committed to solving the murders.
Det Ch Insp Rob Vinson said: 'I don't think any of us can imagine the sheer horror these families have been through over all these years.
"I know this was 30 years ago, but someone may have had their suspicions at the time, or even just recently formed."
A gravely ill father is appealing for information to find the killer of his daughter who was sexually assaulted and beaten to death almost 30 years ago.