A Sydney driver behind the wheel of a luxury car has allegedly been caught with child pornography and illegal drugs.

Police stopped the black BMW in Ultimo to speak with the man about a traffic offence on Tuesday afternoon.

Police say officers searched the car and found methamphetamine and GHB, as well as child abuse material on his mobile phone.

More child pornography on computers and hard drives, as well as more drugs, were later found at a home in Darlinghurst, police said.

The 39-year-old man was charged with two counts each of possessing child abuse material and drug possession. He was refused bail to appear at Central Local Court on Wednesday.