Roy Yearwood was last seen at the Glades Shopping Centre at approximately 3.15pm on Thursday, 10 February.
The 80-year-old suffers from dementia and had recently moved to the Beckenham area from Wembley.
He was last seen wearing a beige and black baseball cap, a blue coat, grey tracksuit trousers and blue trainers.
Anyone with information is asked to call 101 quoting reference 22MIS004791.
Information can also be provided to the Missing People charity.