Kellogg was born in Long Island, the son of the Rev. Samuel Kellogg, a Presbyterian minister and Mary P. Henry Kellogg. Kellogg graduated from Princeton College in 1861; after graduation, he heard Rev.
Henry Martyn Scudder talking about his missionary experience in India and the need for missionaries there. He decided to become a missionary and in 1864, he and his wife, Antoinette Hartwell, sailed for India where they lived and worked at Farrukhabad Mission, Calcutta. After Antoinette's death in 1876, he returned to North America with his four children and worked for the Presbyterian Church of Canada and the Theological Seminary in Allegheny. In 1879, he married Sara Constance Macrum. During this time, his book of Hindi grammar was published and the Council of the British Government's Secretary of State for India prescribed the book as an authority to be studied by all candidates for the India Civil Service as were required to pass examinations in the Hindi language. In 1892 he, Sara and their children travelled to Ahmedabad to retranslate the Hindi Bible. He died in Uttarakhand, India. ==Publications==