The footage shows a violent struggle between the man and several officers in the city’s Skid Row area.
Police say that three officers opened fire after the man tried to grab a gun from an officer.
The dead man, known on the street as Africa, had been homeless after treatment for mental illness.
Skid Row has a large homeless population.
The LAPD said officers had been responding to reports of a robbery and had attempted to use a Taser to subdue the suspect but he had “continued fighting and resisting”.
No other gun was recovered at the scene, LA police commander Andrew Smith said.
Last year, highly publicized killings of black men sparked weeks of protests in the US.
Hours after the latest shooting, the hash tag #LAPDShooting was trending on Twitter in the LA area.
“As if the homeless aren’t victims enough due to economic violence/marginalization, we have cops to shoot them point blank. Ugh,” wrote one tweeter.
Andrew Smith added that at least one of the police officers had been wearing a body camera.
According to an ABC News report, the three officers have placed on leave pending the outcome of an investigation into the shooting.
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