The shirt depicted the U.S. president as a terrorist, the Australian Broadcasting Corp. reported Monday.
Officials at Qantas told Allen Jasson he could not board his flight to London because his T-shirt was offensive and could cause a security risk.
"It's not about affronting anyone and it's certainly not an offensive statement," said Jasson.
He added that he feels President Bush has led an illegal war in Iraq and that it is his democratic right to express a political view.
Melbourne civil liberties advocate Robert Richter said the ban is outrageous.
"You see T-shirts like that on the streets of New York and you don't see American police telling people to take off their T-shirts," he said.
Notable deaths of 2014 [PHOTOS]
UPI Almanac for Sunday, Sept. 21, 2014