Officers are searching for Eric Duffield, who is 39.
He had been in Wakefield visiting his father and left around 10.30am yesterday.
It is thought he was going to catch a bus to Hull but has not been seen since.
A Humberside Police spokesperson said: "We are worried as Eric might be slightly confused due to some medical issues."
He is white, 6ft tall, of large build, and has a bald head. He was wearing a grey hoodie, a Leeds Rhinos rugby top, grey jogging bottoms, a black cap and brown trainers and was carrying a blue carrier bag.
Police are asking anyone who has seen Mr Duffield to get in touch, quoting log 604 of August 19.