Adrian Thomas Fayter was reported missing from his family home in the Hull Road area of city on Saturday 9 April 2011.
Officers are becoming concerned for his welfare and are urging anyone who sees him to get in touch.
PC Andrew Thompson, of York police, said: “We are obviously concerned that Adrian has not been home for over a week now.
“We believe that he has been visiting the Clifton area of York on a daily basis and I would urge local residents to be vigilant and contact the police if they see him.
“The police and Adrian’s family need to know that he is safe and well and I would also urge him to get in touch to confirm he is ok.”
Anyone who can help the police with their enquiries is urged to contact PC Andrew Thompson, of York police, on 0845 60 60 24 7, quoting reference number 121100572