Mubarak Anzi, 32, has the mental age of a 10-year-old and suffers with social anxiety and being in crowded places.
He has been missing since the early hours of Wednesday, August 1.
A spokesperson for West Yorkshire Police said: "His family are incredibly concerned for Mubarak as this is out of character and he would not approach members of the public for help or assistance."
Mr Anzi is described as being of skinny build and about 5ft 7ins. He was last seen wearing a silver jacket with blue on it and black jeans.
Anyone who has seen him or with information about his potential whereabouts is asked to call Bradford District CID via 101, quoting log 179 of 01/08. Information can also be given by using the 101 Live Chat facility on the West Yorkshire Police website.