It happened around 12:45 p.m. Sunday.
Police say a 35-year-old male cab driver for All Threes Taxi company was dispatched to the 800 block of North Markoe Street to pick up a man by the name of "James".
When the driver arrived, police say a man directed him to go to the 5800 block of Race Street.
Once reaching the suspect's destination, police say he grabbed the driver's neck from behind.
When the driver attempted to break free from the suspect he was stabbed several times in his back.
The suspect then exited the vehicle and was last seen heading northbound on North 58th Street from Race Street.
The driver was transported to Penn Presbyterian Medical Center where he was treated for several lacerations.
The suspect is described as a black male, 20 years of age, with a beard, short, thin build, wearing a green hooded sweatshirt and light-colored pants.
A woman living near the stabbing scene told Action News she had no idea the accident in front of her doorstep was about an attempted robbery.
"I didn't know what was going on at first, I just thought it was an accident," the woman said. "And then someone said that the guy was stabbed."
In 2013, a spate of taxi drivers in West and Southwest Philadelphia were victims of attempted robberies.
The most violent happened at Cobbs Creek Parkway and Walnut Street where a driver was shot to death by a patron demanding his money.