It happened in the Ballymagroarty area of Derry in the early hours of Wednesday 10th September.
Investigating the incident, Detective Constable Moyne said: “It was reported that at around 2am, a male youth threatened a female taxi driver as she drove him in her taxi from Rockmills to Carleton Court via Abercorn Road.
“The taxi driver was asked to wait at an address in Abercorn Road whilst the youth entered a house before proceeding on towards Carleton Court where he produced a knife and held it to the driver’s neck and demanded the keys for the car.
“The driver refused to hand the keys over and the youth got out and made off on foot.
“He was described as being around 17 years old, 5’5” tall, of slim build with short dark hair and was wearing a dark blue hooded top.
“I would appeal to anyone with any information about this incident to contact police in Strand Road on the non emergency number 101.
“Information can also be given anonymously through the independent charity Crimestoppers on 0800 555 111.”