An Australian court has denied bail to a 21-year-old Indian cabbie accused of raping a female passenger, who was travelling in his car.

The Melbourne Magistrates court heard Rajveer Singh of Niddrie picked up the 40-year-old woman outside a Richmond pub last November and drove to Northcote, but during the journey he turned off the meter. It is alleged that Singh then parked in the woman's street and raped her.

"The court heard that she was drunk and did not remember the assault, but her son found her on their doorstep half undressed," according to ABC report.

The court further heard that there was a one in 230 billion chance that the DNA evidence linking the taxi driver to the rape of the female passenger was wrong.

The magistrate refused to grant bail to Singh, saying the case against him was strong and he posed a flight risk.