Before becoming a sprinter, Morrow played American football at high school.
Morrow, who had won the 1955 AAU 100 y title, had his most successful season in 1956, which led to his choice by Sports Illustrated as athlete of the year. Morrow won the sprint double in the national college championships and retained his AAU title. Late in the season, Morrow went to Melbourne as a leader of the American sprint team. He came back with three gold medals.
First, Morrow was victorious in the 100 m. Next, he led an American sweep of the medals in the 200 m, equalling the Olympic Record as well. As an anchorman for the 4 x 100 m relay team, he won his third gold, setting a World Record as well.
After the Olympics, Morrow's success on a national level continued, but he retired in 1958. He made a short comeback before the 1960 Olympics, but he failed to qualify for the Olympic team.
After his retirement, Bobby Joe Morrow became a farmer and woodworker.