Christopher Mulligan, 26, was last seen on Thursday, May 25 when he was reported missing from home.
Officers say they are concerned for his welfare and believe he may have been in the Hebden Bridge area on the day he was reported missing.
Police today issued a CCTV image of Mr Mulligan - captured on the day he went missing.
Detective Inspector Craig Lord, of Calderdale CID, said: "From our enquiries, we now know what Christopher was wearing when he was last seen and we believe he may have been in Hebden Bridge that afternoon. Since then we have had no confirmed sightings.
"We know Christopher has previously travelled to Rochdale and Burnley, and believe he has links there.
"I would urgently appeal for anyone who believes they may have seen Christopher to get in touch with police."
Mr Mulligan is described as white, 5ft 6ins tall, with short mousy brown hair and a short brown beard.
He was last seen wearing black trainers, grey tracksuit bottoms and a grey hoodie, with red writing across the chest.
Anyone with information is asked to contact Calderdale CID on 101, quoting log 702 of May 25.