"Get your picture and get out of here, David," a man, reportedly Mr Mack's father, can be heard saying in the background.
"Dad was not impressed with my National Geographic skills," Mr Mack writes in a caption on Instagram.
Mr Mack tells Palm Beach Post he was playing a round of golf with his father when they heard the gator make his catch at the ninth hole.
"We heard a splash and looked down, and the gator had the fish," he says.
Mr Mack claims he was about eight feet from the alligator when he shot the video. The alligator, which can be seen on the putting green close to a lake, was between eight and 10 feet long, he estimates.
"Forget the gator, if there's fish that size at golf courses let's go fishing," writes one person on Instagram.
"Steve Irwin would say 'What a beautiful sight. It's the circle of life, mate,'" writes another.
It's probably safe to assume that alligators have a thing for Florida golf courses. Click for more trending news
For the latest News & Live Updates on Election Results from each assembly constituency in Madhya Pradesh, Rajasthan, Mizoram, Chhattisgarh, Telangana, like us on Facebook or follow us on Twitter for updates.