James Quilter-Adams was last seen in the town at around 11.15pm on Tuesday 30 November 2021.
The 13-year-old is described as being white, around five feet and four inches tall and of slim build with short curly blond hair.
When he was last seen, James was wearing a black jacket with white shoulders and a white hood and zip. He also wore dark grey jogging bottoms and black trainers.
Inspector Mark Stubberfield said: ‘We believe James was in the Bromley area today and he also sometimes travels to areas in Lewisham and Croydon.
‘We are very concerned for his welfare and are urging anyone who sees him or knows where he might be to contact us.’
Anyone with information should call Kent Police on 101, quoting reference number 30-0412.