Jordan Devine, 22, is alleged to have driven a car at Brian McNulty, 32, "at speed" on Jamaica Street on 11 January.
He also faces charges under the Road Traffic Act of failing to stop, and failing to report an accident.
Devine, from Newlands, Glasgow, appeared in private from custody at the city's sheriff court. He made no plea or declaration and was granted bail.
Papers from the court claim that Devine drove a car "deliberately and at speed" at Mr McNulty, causing the car to hit him.
The charges alleges that "as a consequence Brian McNulty was thrown in to the air and landed on the road to his severe injury".
A man has appeared in court charged with attempting to murder another man in Glasgow City Centre.