Over the course of several decades, Gustavo Zepeda found much success in trap shooting in his native Mexico, but the peak of his international career came when his country hosted the Olympics in 1968. He finished 41st out of 55 competitors in the individual trap but, two years later, as part of the Mexican delegation to the 1970 World Championships, he won a silver medal in the team event. He was a member of the Club de Tiro de Pichón and served as its president from 1960 through 1970. He was also president of the Federacion Mexicana de Tiro y Caza briefly in 1992. By career he was involved in the garment industry and served as president of the Cámara Nacional de la Industria del Vestido from 1949 through 1950.