Ashleigh Wallace, 18, was last seen by friends in the Restalrig or Lochend area of the city on Boxing Day.
Miss Wallace,who is 5’8’’ tall, with long black hair, is from the capital’s Northfield area but is also known to frequent Leith.
Of stocky build, Miss Wallace often wears he hair in a ponytail. She has brown eyes.
When last seen she was wearing blue trousers, black jacket, yellow cardigan, cream boots and a black scarf.
Her boyfriend reported her missing on December 27 however there have been no sightings of her and police are appealing for the public’s help.
A spokeswoman for the Lothian and Borders force said: “We are growing increasingly concerned for Ashleigh’s well being, not least because of the current weather conditions.
“She is a vulnerable young woman, who does not have a mobile phone and it is not known if she would have any money in her possession.
“We would appeal for anyone who may have seen her, or who may know where she is, to contact police as a matter of urgency.
“We also want to reassure Ashleigh that she can contact us or Crimestoppers in complete confidence and we would urge her to do that so that we know she is safe and well.”