Surveillance video shows 52-year-old cashier Jorge Grimaldi behind the counter in a dispute with the suspect.
Grimaldi followed the man back to his car and then stood in front of it, appearing to stop the driver from leaving the station. He could be seen dialing on his phone when the driver takes off.
"The driver put the vehicle in drive and proceeded forward," said Det. Bill Bustos of the Los Angeles Police Department. "The clerk jumped onto the hood and the car continued forward for several blocks. At some point, the victim fell off."
That clerk is a married father of two who worked two jobs to support his family. Grimaldi's family members said his condition is improving.
The suspect is described as a black man, about 6 feet tall and 250 pounds. He was driving a red 2009 to 2011 Toyota Camry with a gray interior. Police have a partial California license plate number of 6SNL.
Anyone with information is asked to call the LAPD at (877) 527-3247.