John Peyton Garnett Nelson (June 13, 1873 – March 30, 1930) was an American college football coach and physician. He served as the head football coach at Richmond College—now known as the University of Richmond—in Richmond, Virginia, for one season, in 1901, compiling a record of 1–6. A native of Richmond, Nelson attended the University of Virginia, where he played college baseball as a pitcher. Nelson died of bladder cancer, on March 30, 1930, at St Luke's Hospital in Richmond.