In truth, no one knows who wrote Sir Gawain and the Green Knight. Written many, many years ago, it is amazing that a copy of the poem still exists:
Only a single copy of Sir Gawain and the Green Knight has been preserved from the Middle Ages. The manuscript also contains three other poems, Pearl, Patience, and Purity.
Pearl is about the death of the author's daughter, but the other two pieces are Biblical in nature. This unknown author is often called "the Gawain poet." However, he is also known also as the "Pearl Poet" because of the authorship of "Pearl, an alliterative poem..."
Scholars believe that the writer was educated. "Gawain" was written in Middle English, a form of English popularized (as opposed to Old English) by Geoffrey Chaucer, who wrote The Canterbury Tales, roughly during the same time. The "Gawain" poem appears to have been penned at the end of the 14th Century when the medieval period was already declining.