Police say the victim, described as a man in his late 50s to 60, was walking westbound on Santa Monica Boulevard and crossed Lincoln Boulevard against a red light.
The driver, who had the green light, was heading southbound on Lincoln Boulevard. The driver struck the man, and then fled the scene at about 5:50 a.m.
Jay Kyle, who drives through the area daily on his way to work, said he recognized the victim as a transient who panhandles at the intersection.
"I just saw the guy lying here, and I think it's the same thing he had on two days ago," said Kyle.
While police are still trying to identify the victim, they are asking for the public's help in tracking down the driver behind the crash.
The suspect's vehicle is expected to have damage on the right front passenger side and hood and is missing the right passenger-side mirror. It may be a 2009-2011 charcoal gray Toyota Camry.
The investigation is ongoing. If you have any information regarding this incident, you're urged to contact the Santa Monica Police Department at (310) 458-8495.