The victim hung on to the side of the car as the suspect drove for nearly a mile.
Investigators found part of the victim's foot along Imperial Highway.
The suspect allegedly turned onto the 10900 block of Jackson Avenue trying to throw the victim from the cab, but lost control of the car and sideswiped three parked vehicles.
"It was just a loud noise," said Salvador Franco Jr., whose car was struck in the incident. "I was asleep but it was loud enough to wake me up."
The cab driver, who was in his late 50s, was pronounced dead at the scene.
"The guy, we saw him when he took off running, but nobody was able to catch him at that time," said neighbor Blanca Varela. "I know there was a bunch of money lying on the floor. It was really devastating."
The suspect fled the scene.
"We're looking at it right now as probably some type of robbery that went bad," said Lt. Don Slawson with the Los Angeles County Sheriff's Department.
The victim's family said he experienced other robbery attempts but managed to fight them off.
Family members said he loved being a cab driver. He was a cab driver for more than 15 years, they said.
He leaves behind five children and a wife.
Anyone with information is urged to call the Los Angeles County Sheriff's Homicide Bureau at (323) 890-5500.