Freya Cook, who is 14 years old, was last seen in the town centre at around 8.45pm on Sunday 25 October 2020.
Freya is white, around 5 feet tall, of slim build and with long straight blonde hair.
When she was last seen she was wearing a dark blue padded jacket with a fur trim and belt, dark jeans and black trainers.
Detective Inspector Catherine Ruler of Medway police said: ‘We are concerned for Freya’s welfare and would urge anyone who may have seen her or knows where she may be to call us.’
Anybody with information should call Kent Police on 101, quoting reference 26-0325.