Dhiraj Jetha is last known to have been the High Street area of Rochester walking towards Chatham at around 12.10pm on Wednesday 12 May 2021.
The 61-year-old is described as being around five feet and eight inches tall, of slim build and with a shaven head.
He is thought to have been wearing tracksuit bottoms, a jumper and pink slider footwear.
Inspector Kevin Lincoln from Medway Police said: ‘We are concerned for Mr Jetha’s 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 12-0682.