A Sydney Uber driver who claimed a drunk young woman asked him for sex has been found guilty of raping her in the back seat of his car.

Muhammad Naveed, 41, faces a maximum 14 years' jail after a jury found he had non-consensual sex with a woman he picked up in King's Cross on a Saturday night in October 2015.

It took only hours for them to deliver the guilty verdict against Naveed, who initially told police it was "consent sex".

He sat emotionless at Downing Centre District Court as Justice Deborah Payne refused his application for bail prior to sentencing on Wednesday.

The court heard the woman had been drinking with friends at several venues before getting into what she thought was a cab to go home.

While driving to the eastern suburbs, where the woman lived, Naveed pulled into a service station and bought condoms and a bottle of water.

He then drove in the opposite direction to her home, stopped in a side street and asked if she wanted to move to the back seat.

"The complainant will tell you at this point she could not keep her eyes open and she was falling asleep," crown prosecutor James Trevallion said during the trial.

The next thing the woman remembers is waking up to find Naveed on top of her.

"She did not have enough strength to push him off," Mr Trevallion said.

Afterwards, Naveed drove her home and she fell asleep on the way.

At home, she phoned a friend, who then called police.

Naveed was arrested a few days later and told investigators it was "consent sex".

He later testified the woman had asked him for sex but they didn't have intercourse because he couldn't get aroused.

Naveed said he had given her a lift out of "sympathy" even though she had no money and wouldn't be able to pay until the next day.

He is set to be sentenced in Parramatta District Court on May 5.