Tony Moore was 24 years old at the time of the 1976 Summer Olympics, competing in his only Olympics. He competed in the men's 100 metres on 23 July where in heat nine he finished last with a time of 11.16 seconds. Two days later on 25 July, he competed in the heats of the men's 200 metres finishing in fourth place in the sixth heat. In the quarter-finals he competed in the third quarter final. He would go on to finish in seventh place in his heat being almost six tenths ahead of last place runner, Abdul Aziz Abdul Kareem from Kuwait. After not starting the 400 meters event on 26 July, his final event was the long jump with qualifying being held on 28 July. In his qualifying group he finished in 15th place in Group B and 31st overall with a jump of 6.81 metres.