Public Safety Director Dennis Brown says the alligator was spotted around 3 p.m. Wednesday.
Angus McBride with the Department of Natural Resources says it's not unusual for alligators to get caught in tidal waters and end up in the ocean. McBride said alligators do not like salt water.
Alligator specialist Ray Covington with Nuisance Removal Wildlife Service shot the gator in the head and hauled it away.
Some people complained about shooting the alligator on the beach but Covington says the animal was sick and was too large to relocate.
He says it would have been too dangerous to try to remove the alligator and shoot it elsewhere.