The crash occurred near the intersection of Manchester Avenue and Figueroa Street at about 3:40 a.m., Los Angeles police said.
LAPD said the victim, 61-year-old Wardell Nelson Jr., was crossing eastbound Manchester Boulevard at Figueroa Street on the south side crosswalk when he was struck by a fleeing driver in an unknown vehicle.
Another vehicle hit Nelson as he "laid motionless on the ground," but that driver remained on the scene, police said in a news release.
Nelson died at the scene.
Relatives of Nelson say he had been living on the streets by his own choice.
They say they are shocked and upset a driver struck him and left him in the street, but hope police receive information that leads to an arrest.