Matthew Kesbey was last seen in the South Road area of Faversham at around 11.45am on Saturday 5 June 2021.
The 48-year-old is described as white, approximately five feet eleven inches tall, medium build and with short grey hair.
He was last seen wearing a brown beanie hat, brown top, brown coat, and navy blue jeans. He left on foot and may be seen carrying a blanket and a pillow.
Anyone with information is asked to call Kent Police on 101 quoting reference 05-0501.