Jim McIlwain, 40, was last seen at his home in Farsley at about 2pm yesterday (Monday).
Police now say they are concerned for his welfare.
They have appealed for anyone who sees Mr Mcllwain to get in touch.
Detective Inspector James Entwistle, of Leeds District CID, said: “We are very concerned for his welfare and urgently need to find out where he is so we can check he is okay.
“We would like to hear from anyone who has seen him or who has any information that could assist us in tracing him.”
He is described as white, bald, 6ft tall, medium build, with hazel brown eyes.
Mr Mcllwain was last seen wearing light-coloured jeans, a khaki sweater, a tan leather jacket and brown Timberland style boots.
He has tattoos including a tribal pattern on the lower half of his right arm and a faint tattoo on his left hand. He has a mole on the right side of his mouth and a pierced nose and left ear. He also wears grey Superdry glasses and has a "West Country" accent.
Anyone with information is asked to contact the Special Operations Room at Elland Road via 101, quoting log number 1919 of March 19.