A son of motor racing champion Jack Brabham has been found guilty of raping a six-year-old girl.

Gary Thomas Brabham, 54, was convicted in the Brisbane District Court of one count of rape and one count of the indecent treatment of a girl under the age of 12.

The offences occurred between 2003 and 2007.

The girl's mother took her daughter to police after she told her of the abuse in October 2013.

Brabham was found not guilty of another five counts of indecent treatment.

After the verdicts were handed down, the court was told Brabham had a criminal history.

Brabham followed his famous father into motor racing making a name for himself in Europe, but did not make it on the Formula One circuit after he failed to pre-qualify for the first two races of the 1990 season before quitting.

He was the first Australian to race in the Gold Coast Indy Car event.