Named only as Brian, he vanished from Dudley's Russells Hall Hospital on the morning of Sunday, June 26.
Dudley Police, who initially launched an appeal to find him on Monday, say the 64-year-old has connections to the Blackheath area.
Brian is described as 6ft tall with cropped hair and was last seen wearing a blue cardigan, black T-shirt, jeans and black shoes.
Renewing their appeal to find Brian on Sunday, the force said: "We still need your help finding Brian. This CCTV image of him is from the day he went missing.
"He's also got links to Bewdley."
Anyone who sees Brian is asked to quote call 999 and quote PID 414762 while anyone with information that can help find him is asked to contact West Midlands Police using Live Chat on the force's website or by calling 101.