Edward Sheffield Nelson (born April 23, 1941) is an American attorney, businessman and politician from the capital city of Little Rock, Arkansas.

He graduated from Brinkley High School and thereafter received his undergraduate degree in mathematics education from the University of Central Arkansas at Conway, where he was the student body president.

In 1990, Nelson won the Republican gubernatorial nomination in a divisive race against Tommy F. Robinson, who then held Arkansas's 2nd congressional district seat based about Little Rock.

In 1994, he sought the governorship again and narrowly won the GOP primary over state Senator Steve Luelf and businessman Bill Jones.

Nelson is the fourth Arkansas Republican whom Bill Clinton defeated for governor; the others being Lynn Lowe, Frank D. White, and Woody Freeman.