Debbie Linsley, 26, was stabbed to death on the 2.16pm train from Orpington to Victoria Station on Wednesday 23 March 1988.
She was found lying on the floor of the carriage in a pool of blood when the train arrived at platform 2 at around 2.50pm.
Debbie, who was working as a hotel manager in Edinburgh, had suffered at least five stab wounds, including a fatal injury to her heart, and defence wounds to her hands suggested she bravely tried to fend off her attacker.
Although detectives believe they have found a DNA profile of her killer from blood left at the scene, nobody has ever been arrested and the case remains unsolved.
A £20,000 reward is on offer for information leading to the arrest, charge and prosecution of the person or persons responsible for the murder.
Debbie's father, Arthur Linsley, said: "When Debbie was murdered the Senior Investigating Officer described the attack as savage and brutal. She was stabbed at least five times and because of the severity of the attack he was of the opinion that it was unlikely that this was the culprit's first violent offence.
"Debbie had deep defence wounds on her hands but despite this she injured him during the struggle.
"As a result of this a full DNA profile has subsequently been obtained of the attacker. So here we have a probable repeat violent offender and we have his full DNA profile but he is not on the DNA Database. I find that very puzzling.
"There must be a partner, relative or friend out there who knows of someone who returned home with an unexplained injury and we are appealing for that person or persons to come forward. After all we only need one phone call if it is the right one."
Debbie had been visiting her parents and her brother Gordon as part of the preparations for Gordon's wedding a few weeks later.
She caught the train at Petts Wood and boarded a six-person compartment with doors at each side of the carriage.
A French passenger later told police she heard screaming on board the train after it left Brixton.
The murder weapon has not been recovered but is thought to have been a heavily bladed knife with a length between five and seven and a half inches.
Detectives are trying to use state of the art DNA techniques to try and identify the killer from a blood sample left at the scene.
Detective Chief Inspector Chris Burgess, Head of Specialist Crime Review Group, said: "Twenty five years on from the murder of Debbie Linsley, an innocent woman on a train in broad daylight, we are still hopeful that the murderer can be caught.
"The passage of time has not diminished the shocking nature of this crime; it has just made it harder to bear for her loved ones, when justice has not been achieved.
"We still believe there are people out there with information that could be vital to a breakthrough in the case.
"I would urge those people to call us. I can assure them that they will be dealt with sensitively."
Contact the incident room on 0207 230 3893 and 0207 230 0992 or Crimestoppers on 0800 555 111.