George was the son of Jay Gould (1836–1892) and Helen Day Miller (1838–1889). He married Edith M. Kingdon (1864–1921), a stage actress, and had the following children:
Kingdon Gould, Sr. (1887–1945) who married Annunziata Camilla Maria Lucci (1890–1961)
Jay Gould II (1888–1935) who was a tennis player and who married Anne Douglass Graham