Sussex Police are looking for Malcolm Mason, who was last seen on Tuesday (September 29).
The 49-year-old is described by police as a white male, of a heavy build, with light brown balding hair, he wears glasses and has blue eyes.
He was last seen in Chippenham, Wiltshire, and has links to Worthing and West Sussex, police said.
He may be using the rail network to travel.
Police are concerned for his welfare and ask members of the public not to approach Malcolm if he is seen but to call 999 immediately quoting 47200169926.