The shooting happened outside a convenience store on Bissonnet Street near E A Olle Middle School around midnight, Houston police said.
Investigators said the man was shot multiple times in the chest while trying to take a cellphone from a man with a gun.
Police said the man who fired the shots stayed at the scene and was talking to investigators about what happened.
The man who was shot was taken to an area hospital in "grave condition," Lt. J.P. Horelica said.
It was unclear if charges would be filed.