His father was a wealthy farmer, a slaveholder, and county judge in Virginia. Both parents were Methodists, formerly Episcopal and Presbyterian. Moncure's opposition to slavery came from his mother and from his boyhood experiences. His father and three brothers remained staunchly pro-slavery. He graduated at Dickinson College in 1849, studied law for a year, and then became a Methodist minister. In 1852, thanks largely to the influence of Ralph Waldo Emerson, his religious and political views underwent a radical change he fell under the influence of "transcendentalism," and became an outspoken abolitionist.
After graduation from Harvard, Conway was ordained in 1855 but his anti-slavery views brought about his dismissal in 1856. His abolitionist stance and the attempt to rescue the fugitive slave, Anthony Burns, in Boston, Massachusetts, aroused the hostility of his old neighbours and friends. From 1856 to 1861 he was a Unitarian minister in Cincinnati, Ohio. After the Civil War broke out, Conway located several dozen of his father's slaves in Washington, DC, who had fled from Virginia, and escorted them through Maryland, still a slave state, to safety in Ohio. While in Cincinnati, Conway married Ellen Davis Dana. Ellen was a Unitarian, a feminist and an abolitionist. The couple had four children.
He became editor of the Commonwealth in Boston, and wrote powerful pleas for emancipation. In 1863, Conway was asked by American abolitionists to go to London to convince the UK that the American Civil War was a war of abolition. Under English influence, Conway eventually contacted the Confederate States of America "on behalf of the leading antislavery men of America" offering the preservation of the Confederacy after the war's end in exchange for emancipation of the slaves. His support by his sponsors was quickly and angrily withdrawn. He went to Venice for a while.
Upon return to London, he became the minister of the South Place Chapel, Finsbury, London. The congregation that met there had began in 1793, as a group of nonconformists known as Philadelphians or Universalists. William Johnson Fox, a former theological student of Dr Pye Smith, became minister in 1817. In 1824 the congregation built the chapel at South Place. During the first period that Conway led the Society, 1864-1884, the congregation moved away from unitarianism. In 1864, he abandoned theism after one of his sons died. His thinking continued to move from Emersonian transcendentalism toward a more humanistic "freethought". During this time, Conway wrote frequently for the London press. In 1868 Conway was one of four speakers at the first open public meeting in support of women's suffrage in Great Britain.
In 1885 Conway returned to the US for some years, where he spent the time researching the first biography of Thomas Paine. The post of minister at South Place was handed over to a fellow American, Stanton Coit. During this period the name of the Society was changed from South Place Religious Society to South Place Ethical Society. Conway returned for a second term as minister in 1892-1897.
In 1897 his wife Ellen became terminally ill and wished to die in the United States of America, so they returned to New York. As the Spanish - American War approached, Conway became disaffected with his countrymen. He moved to France to devote much of the rest of his life to the peace movement and writing. Conway died alone in his Paris apartment in 1907. In 1926 the South Place Ethical Society built new premises at 37 Red Lion Square in Holborn, and called it Conway Hall in his honour. The name of the society continued to reflect the original location until in 2012 it was renamed the Conway Hall Ethical Society.