The Daily Times of Maryville reported his death was the fourth fatality this year on the 11.1-mile stretch, which contains 318 curves. The section of highway, which extends into North Carolina, attracts motorcycle riders from across the country and is also known as Deal's Gap.
Green was riding with his son, John Green, and four other friends.
The newspaper quoted one of Green's friends saying they were trying to be careful, but he described the road as "a beast."
The highway forms the southern boundary of the Great Smoky Mountains National Park.
Since 1995, at least 25 motorcyclists have been killed on the highway.