Barrie Lumsden was last seen in the Kingswood Road area of the town at around 3pm on Friday 3 March 2023.
The 88-year-old is described as around 5ft, 8ins tall and of a slight build, with a white beard and glasses.
He is believed to be wearing a dark-coloured cap, a navy blue raincoat and black trousers. He may be carrying a walking stick.
Officers are concerned for his welfare and urge anyone who has seen him to call 101, quoting reference 03-1157.