The graphic video, which was posted on Facebook, shows a violent altercation between a man and several officers in LA’s Skid Row area near downtown.
The circumstances around the shooting were not immediately clear but the video appears to show a man flailing at officers as they try to subdue him.
A voice yelling “Drop the gun!” can be heard before several shots ring out and several onlookers cry out in alarm.
The Los Angeles Police Department didn’t immediately return a call for comment, but local media said at least one officer had opened fire.
The man was declared dead at a hospital soon after the shooting, police spokesman Sergeant Barry Montgomery told the Los Angeles Times.
Skid Row is a run-down area that houses many hostels and services for the region’s homeless people, some of whom pitch tents on the sidewalks.
Officers were responding to a robbery call and a witness said the victim had been fighting with someone in his tent, the Times reported.
The video comes against a backdrop of highly publicized police shootings of black men that sparked weeks of protests late last year.
A local CBS television affiliate reported that tensions in the area remained high for hours after the shooting.
The video also shows police grabbing a woman after she picks up a baton that an officer dropped, then appears to raise it.
The video can be viewed on this Facebook page: http://u.afp.com/Hyn