Born in McKinney, Texas, Smith moved to California when he was a kid. He was originally a high jumper, but UC Berkeley, the university he wanted to attend, already had a strong high jumping team, so he took up pole vaulting. He won the NCAA championships in 1941, the year before he graduated as a history major. During the remainder of World War II, Guinn Smith served as an air force pilot in Asia.
Smith, the 1947 national pole vault champion, was sent to the 1948 Olympics in London. During a rainy competition, Smith took the gold in his last attempt for 4.30 m (14 ft 11⁄4 in).