The officer-involved shooting, which happened at the METRO Transit Center in downtown near Travis and Pierce on Tuesday, was captured on the bus' on board camera.
Acevedo said the suspect had beaten the female guard at nearby Legacy nightclub.
The suspect then took the guard's gun and ran toward the transit center, where the guard flagged down the officer.
WATCH: Chief Art Acevedo offers details into officer-involved shooting at METRO Transit Center
The chief said the officer, who was heading home at the time, confronted the suspect who had gotten on a bus.
The officer demanded the suspect drop the weapon, but then opened fire after the man did not comply, Acevedo said.
The suspect died at the scene. The off-duty officer, who wasn't immediately identified, was not hurt in the incident.
An investigation continues into the shooting.
Chief @ArtAcevedo and commanders are on scene of an HPD officer-involved shooting at 1900 Travis St. Preliminary info is the suspect was struck and is deceased. No officers are injured. Additional information to be released at the scene. PIO is en route. #hounews— Houston Police (@houstonpolice) August 4, 2020