Burgess told Good Morning America he went for an early-evening jog on a trail he's visited often. He pulled out his phone to take a video when he came across what he thought were wild kittens.
WATCH | Kyle Burgess talks about his encounter on "Good Morning America"
That's when he noticed the cougar lurking behind and he started backing away.
"I came upon the cubs, and that's when I obviously pulled out my phone, to take pictures of the wildlife," Burgess said. "Once I realized it was a mountain lion, she started chasing after me."
What ensues is a six-minute standoff, with the animal stalking Burgess and lunging at him with its claws bared as he tries to scare it away with loud noises.
"Go away! Go away!" he yells at one point. Then, as a sort of self-affirmation, he says: "I'm big and scary."
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At one point the cougar lunged at Burgess when he briefly turned his back.
"She got within four feet of me," Burgess said.
Burgess eventually throws a rock at the big cat, which then finally flees. Burgess was not harmed.
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Burgess later shared the heart-stopping footage on Instagram, where it has been viewed more than 132,000 times.
"Sorry, not sorry for the language," the video's caption says. "I thought I was done for!"