Gulliver's Travels was first published in 1726. The author of the work is Jonathan Swift. Jonathan Swift is the official writer of Gulliver's Travels. Perhaps your question is asking something different though. While Jonathan Swift wrote the story, Jonathan Swift is not the narrator of the story. Gulliver's Travels is written in the first person perspective. That means the narrator of the story is a character in the story. In this case, the narrator of Gulliver's Travels is Lemuel Gulliver himself. He narrates the story through a first person perspective, and he narrates it in the past tense.
Even though Jonathan Swift is the man that put pen to paper for the story, I suppose that an argument could be made that the writer of the story is actually the fictional Gulliver.