Joseph David Green is an American former professional football player who was a defensive back and return specialist for the New York Giants of the National Football League (NFL). He played college football for the Bowling Green Falcons, earing Mid-American Conference Defensive Player of the Year honors in 1969 as a senior. He was undrafted in 1970 and picked up that year by the Giants. Green played for the Giants for two seasons, and returned seven kickoffs for 132 yards. He started in two games on defense in 1971, and recorded the only touchdown of his pro career that year as he returned a fumble for a score against the Green Bay Packers. He is the father of former NFL player Barrett Green.