"I said, 'Don't mess with Nana,'" Cochran told KTRK. "My grandchildren call me Nana."
The hunt took place in the same pond where her 5-year-old grandson, Simon Hughes, killed an alligator in 2009.
Cochran explained that the reptile that was dispatched Monday was suspected of killing one of her miniature horses on her ranch, which is why she set out to kill the alligator.
"We think this is the gator that ate one of our miniature horses several years ago, as big as this gator was, he could've easily eaten it," Cochran told KTRK. "Typically the gators don't bother us, but we've been looking for (this one)."
Cochran had to wait until Sept. 10 to go after the alligator, when a 20-day hunting season began.
"There are a lot of requirements to kill a gator in Polk County," she told the Chronicle. "You have to have a permit and tags from a wildlife biologist, and you have to catch it on a hook first. We don't just go to the ranch and hunt a gator."
Cochran said the alligator's head would be mounted in her office. The family will eat the meat, and the tide will be tanned to make some boots, Cochran told the Chronicle.
"I became mayor in May, became a great-grandmother on Friday, killed the gator on Monday," Cochran told KPRC.
What is her next adventure?
“I'm going to see what I can get into next," Cochran told the television station, laughing.