Panicked travellers scrambled to escape after the shooter -- identified as 23-year-old Paul Anthony Ciancia -- armed with an assault rifle, blasted through a security checkpoint at the airport shortly after 9:00 am (2130 IST) yesterday.
Ciancia then walked calmly through the terminal seeking further victims. He was eventually stopped when police shot and wounded him.
TV footage showed people diving to the floor at the sound of gunfire and scrambling to escape the terminal.
The lone gunman, who reportedly had a grudge against the TSA, also wounded seven people in the rampage.
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But he was still carrying plenty of ammunition when he was arrested, said Los Angeles Mayor Eric Garcetti.
"There were more than 100 more rounds that could have literally killed everybody in that terminal today," he said, praising airport police. "If it were not for their actions, there could have been a lot more damage," he said.
The shooter opened fire in a crowded terminal of the country's third-busiest airport.
He "came into Terminal Three, pulled an assault rifle out of a bag and began to open fire," said Patrick Gannon, head of the airport police.
"He proceeded up into the screening area ... And continued shooting," he said.
Police chased the gunman, "engaged him in gunfire... And were able to successfully take him into custody."
The FBI later named the shooter, and said that he was a Los Angeles resident originally from the eastern state of New Jersey.
Police found a note on the gunman voicing "disappointment in the government" but that he did not want to harm "innocent people," a law enforcement official told the Los Angeles Times newspaper.