Robert Laming is last known to have been in the Mierscourt Road area at around midday on Thursday 13 May 2021.
The 39-year-old is described as being around five feet and eight inches tall, of large build and with short brown hair.
When he was last seen, Robert was wearing trousers and a pink shirt.
Inspector Dan Blatter said: ‘Robert is believed to be on foot in the Medway Towns area. We are concerned for his welfare and are urging anybody who sees him or knows where he might be to contact us.’
Anyone with information is asked to call Kent Police on 999 quoting 13-0612.