Dramatic video shows Nikye Thomas, 19, grappling with a man over a small bag on 24 June. He then brazenly pulls out a gun, leading the other man to flee.
Police are alerted and a chase through the city follows. CCTV shows the teen dropping the gun in Burlington Arcade.
Officers continued to sprint after him into Birmingham New Street, where an officer takes him down and arrests him with the help of an off-duty officer.
Thomas has been jailed for five years.