Sophie Smith went missing around 3am on Boxing Day (26 December 2017) from her address in Avondale Road in the town.
Sophie is described as being white, about 5ft 8, of a slim build with shoulder length blonde hair. It is believed she was wearing a dark coloured vest top and light coloured shorts.
Officers are keen to hear from anyone who may have seen Sophie or knows of her current whereabouts.
Anyone with information should contact Norfolk Police immediately on 101.