Authorities said the children hooked a noose around the gator at Fay Lake Wilderness Park in Port St. John and dragged it to shore Thursday night.
The 16-year-old was issued a citation for feeding, enticing or molesting alligators, Florida Wildlife Commission spokesperson Chad Weber.
The other two children are 6 and 8 years old and were not given any citations. Authorities said the vacationers were not familiar with local gator laws.
The gator had already returned to the water with the noose still around its neck when officials arrived. BCSO reports a trapper was called out to remove the rope. The alligator was also picked up for public safety, and was later euthanized.