Richard Lindsay, 56, went missing from his home in Scarborough on Tuesday, December 10.
He was last seen in Rotherham, South Yorkshire on Friday, December 13 and was reported missing the next day.
Officers believe he could be travelling throughout Yorkshire, probably on public transport.
He is described as vulnerable and police are concerned about his welfare during the recent spell of cold weather.
Mr Lindsey, pictured, is of medium build with grey hair, green eyes and a ruddy complexion.
He may be moving around West Yorkshire, South Yorkshire or Humberside and officers are trying to find him to ensure he is safe.
Anyone with information is asked to contact North Yorkshire Police on 101, select option 1 and quote reference 12190228699.