Craig was born on a farm in Daviess County, Kentucky, likely on 1 December 1867. His parents, Dempsey Craig and Mary Roberts, were not married. His father later married at least four times, and he had many half-siblings.

Craig married Nancy “Nannie” (née Wallace) Kirk on 19 January 1890 in Fordsville, Ohio County, Kentucky. The couple had five children together, as well as Nancy’s three children from her previous marriage; three of them outlived their father.

In around 1911, the family moved to Benton, Illinois, and later to the nearby city of Harrisburg. Craig worked as a miner for 36 years near Eldorado, as well as at Western Cartridge Co., which later became Olin Corp. in Alton.

Craig’s wife Nancy died in 1928. In his later years, Craig was affectionately known as ‘Pappy’. He survived pneumonia at the age of 109. As a supercentenarian, he had 13 grandchildren, 30 great-grandchildren, and five great-great-grandchildren.

Craig died on 14 March 1978 at the likely age of 110 years, 103 days. After Charlie Nelson, he was the second-oldest known man in the United States and the world.