Among the injured, one is in critical condition, Louisiana State Police Master Trooper Michael Reichardt said at a news conference, Xinhua reported.
The shooting took place around 1:00 a.m. local time (0600 GMT) on Sunday on the campus quad, according to social media posts from the university.
The person who died wasn't enrolled at the school, and only one of the injured was a student, who was treated for non-fatal injuries, said an ABC News report.
In the wake of the shooting, the university set a curfew from 9:30 p.m. to 6:00 a.m. until further notice, said the report, adding that homecoming events on Sunday, as well as classes on Monday and Tuesday, have been canceled.
It's the second deadly shooting on campus in only four days after one person was killed and three others wounded in a separate shooting on Wednesday. Police do not believe the incidents are connected at this time.
Louisiana State Police said in a news release Sunday evening that investigations into the two shootings are underway.
Grambling State University, which opened in 1901 as the Colored Industrial and Agricultural School, is a historically Black university located in northeast Louisiana.
RHM/PR