The officer responded to a call of shots fired on Martin Luther King drive shortly before 2 a.m. Saturday.
He says he spotted Deron Kittrell, 28, with a gun and ordered him to freeze.
Instead, police say Kittrell ran then allegedly turned and aimed the gun at the officer.
The officer shot Kittrell four times.
The grandmother of his children Donalda James says she's upset with how police handled the situation.
"We're in shock right now. We don't even really know how to process this. We don't know what to tell the kids. I'm sure it could've been handled differently, even if he did run," James said.
Police say they found shell casings at the scene from a 9-millimeter gun, the same type of gun they say Kittrell had.
The incident will be reviewed by the prosecutor's office.