The shooting happened at about 11:50 p.m. outside the Pittsburg Health Center at 2311 Loveridge Road.
Three homeless men had been seeking shelter on benches outside the clinic when the gunman approached two of them.
The gunman ordered the victims to surrender their property and to get down on the ground, Addington said.
The victim, a 44-year-old man, got down on the ground but didn't have any property to surrender, Addington said.
Some sort of verbal exchange took place between the victim and the suspect and then the suspect shot the victim twice as he lay on the ground.
The other two men were not injured. They described the gunman as a black man in his late teens or early 20s. He was about 6 feet tall with a slender build and wearing light-colored pants and a dark shirt.
Police know the victim's name, but weren't yet releasing it early this afternoon because his family had not yet been notified of his death, Addington said.