They say it is out of character for Tim Mercer, 50, who was last seen at the Tesco Express store on Stanley Road, Wakefield, at around 6pm on Tuesday, September 20.
Mr Mercer lives in the Eastmoor area and despite extensive police enquiries to trace him, Tim has not been seen since.
Det Insp Dan Tillett, of Wakefield CID, said: “It is now two months since Tim was last seen and we are very concerned for his welfare as this is out of character for him.
“His family are naturally desperate to know he is safe and I would urge Tim or anyone who has any information about his whereabouts to get in touch.”
Tim is described as a white, 5ft 8in tall, with a scar to his left cheek and a beard. He was last seen wearing a black beanie hat with a Leeds United emblem on the front. He speaks with a Yorkshire accent.
Anyone with any information should contact DI Dan Tillet in Wakefield CID via 101, quoting reference 13160418014.